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Results 1 - 25 of 32 |
1. CMB Online first
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Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds Let $\Gamma_1$ and $\Gamma_2$ be Bieberbach groups contained in the
full isometry group $G$ of $\mathbb{R}^n$.
We prove that if the compact flat manifolds $\Gamma_1\backslash\mathbb{R}^n$ and
$\Gamma_2\backslash\mathbb{R}^n$ are strongly isospectral then the Bieberbach groups
$\Gamma_1$ and $\Gamma_2$ are representation equivalent, that is, the
right regular representations $L^2(\Gamma_1\backslash G)$ and
$L^2(\Gamma_2\backslash G)$ are unitarily equivalent.
Keywords:representation equivalent, strongly isospectrality, compact flat manifolds Categories:58J53, 22D10 |
2. CMB Online first
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Alexandroff Manifolds and Homogeneous Continua ny homogeneous,
metric $ANR$-continuum is a $V^n_G$-continuum provided $\dim_GX=n\geq
1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal
domain.
This implies that any homogeneous $n$-dimensional metric $ANR$-continuum is a $V^n$-continuum in the sense of Alexandroff.
We also prove that any finite-dimensional homogeneous metric continuum
$X$, satisfying $\check{H}^n(X;G)\neq 0$ for some group $G$ and $n\geq
1$, cannot be separated by
a compactum $K$ with $\check{H}^{n-1}(K;G)=0$ and $\dim_G K\leq
n-1$. This provides a partial answer to a question of
Kallipoliti-Papasoglu
whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.
Keywords:Cantor manifold, cohomological dimension, cohomology groups, homogeneous compactum, separator, $V^n$-continuum Categories:54F45, 54F15 |
3. CMB Online first
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Erratum to the Paper "A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold" We correct two clerical errors made in the paper "A Lower Bound for
the Length of Closed Geodesics on a Finsler Manifold".
Keywords:Finsler manifold, closed geodesic, injective radius Categories:53B40, 53C22 |
4. CMB Online first
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Addendum to ``Limit Sets of Typical Homeomorphisms'' Given an integer $n \geq 3$,
a metrizable compact topological $n$-manifold $X$ with boundary,
and a finite positive Borel measure $\mu$ on $X$,
we prove that for the typical homeomorphism $f : X \to X$,
it is true that for $\mu$-almost every point $x$ in $X$ the restriction of
$f$ (respectively of $f^{-1}$) to the omega limit set $\omega(f,x)$
(respectively to the alpha limit set $\alpha(f,x)$) is topologically
conjugate to the universal odometer.
Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets Categories:37B20, 54H20, 28C15, 54C35, 54E52 |
5. CMB Online first
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A lower bound for the length of closed geodesics on a Finsler manifold In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.
Keywords:Finsler manifold, closed geodesic, injective radius Categories:53B40, 53C22 |
6. CMB Online first
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On the continuity of the eigenvalues of a sublaplacian We study the behavior of the eigenvalues of a sublaplacian $\Delta_b$ on a compact strictly pseudoconvex CR manifold $M$, as functions on the set
${\mathcal P}_+$ of positively oriented contact forms on $M$ by endowing ${\mathcal P}_+$ with a natural metric topology.
Keywords:CR manifold, contact form, sublaplacian, Fefferman metric Categories:32V20, 53C56 |
7. CMB 2011 (vol 56 pp. 173)
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Semi-invariant Submersions from Almost Hermitian Manifolds We introduce semi-invariant Riemannian submersions from almost
Hermitian manifolds onto Riemannian manifolds. We give examples,
investigate the geometry of foliations that arise from the
definition of a Riemannian submersion, and find necessary sufficient
conditions for total manifold to be a locally product Riemannian
manifold. We also find necessary and sufficient conditions for a
semi-invariant submersion to be totally geodesic. Moreover, we
obtain a classification for semi-invariant submersions with totally
umbilical fibers and show that such submersions put some
restrictions on total manifolds.
Keywords:Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion Categories:53B20, 53C43 |
8. CMB 2011 (vol 55 pp. 632)
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Characterizations of Model Manifolds by Means of Certain Differential Systems We prove metric rigidity for complete manifolds supporting solutions of
certain second order differential systems, thus extending classical works on a
characterization of space-forms. Along the way, we also discover
new characterizations of space-forms. We next generalize results concerning metric
rigidity via equations involving vector fields.
Keywords:metric rigidity, model manifolds, Obata's type theorems Category:53C20 |
9. CMB 2011 (vol 55 pp. 225)
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Limit Sets of Typical Homeomorphisms Given an integer $n \geq 3$, a metrizable compact
topological $n$-manifold $X$ with boundary, and a finite positive Borel
measure $\mu$ on $X$, we prove that for the typical homeomorphism
$f \colon X \to X$, it is true that for $\mu$-almost every point $x$ in $X$
the limit set $\omega(f,x)$ is a Cantor set of Hausdorff dimension zero,
each point of $\omega(f,x)$ has a dense orbit in $\omega(f,x)$, $f$ is
non-sensitive at each point of $\omega(f,x)$, and the function
$a \to \omega(f,a)$ is continuous at $x$.
Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets Categories:37B20, 54H20, 28C15, 54C35, 54E52 |
10. CMB 2011 (vol 55 pp. 164)
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Involutions Fixing $F^n \cup \{\text{Indecomposable}\}$ Let $M^m$ be an $m$-dimensional, closed and smooth manifold, equipped with a smooth involution $T\colon M^m \to M^m$ whose fixed point set has the form $F^n \cup F^j$, where $F^n$ and $F^j$ are submanifolds with dimensions $n$ and $j$, $F^j$ is indecomposable and $ n >j$. Write $n-j=2^pq$, where $q \ge 1$ is odd and $p \geq 0$, and set $m(n-j) = 2n+p-q+1$ if $p \leq q + 1$
and $m(n-j)= 2n + 2^{p-q}$ if $p \geq q$. In this paper we show that $m \le m(n-j) + 2j+1$. Further, we show that this bound is \emph{almost} best possible, by exhibiting examples $(M^{m(n-j) +2j},T)$ where the fixed point set of
$T$ has the form $F^n \cup F^j$ described above, for every $2 \le j Keywords:involution, projective space bundle, indecomposable manifold, splitting principle, Stiefel-Whitney class, characteristic number Category:57R85 |
11. CMB 2011 (vol 54 pp. 396)
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Parabolic Geodesics in Sasakian $3$-Manifolds We give explicit parametrizations for all
parabolic geodesics in 3-dimensional Sasakian space forms.
Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds Category:58E20 |
12. CMB 2011 (vol 54 pp. 716)
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Symplectic Lie-Rinehart-Jacobi Algebras and Contact Manifolds We give a characterization of contact manifolds in terms of symplectic
Lie-Rinehart-Jacobi algebras. We also give a sufficient condition for a Jacobi
manifold to be a contact manifold.
Keywords:Lie-Rinehart algebras, differential operators, Jacobi manifolds, symplectic manifolds, contact manifolds Categories:13N05, 53D05, 53D10 |
13. CMB 2010 (vol 53 pp. 674)
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Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
We study a semilinear elliptic problem on a compact Riemannian
manifold with boundary, subject to an inhomogeneous Neumann
boundary condition. Under various hypotheses on the nonlinear
terms, depending on their behaviour in the origin and infinity, we
prove multiplicity of solutions by using variational arguments.
Keywords:Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions Categories:58J05, 35P30 |
14. CMB 2010 (vol 53 pp. 684)
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An Isospectral Deformation on an Infranil-Orbifold
We construct a Laplace isospectral deformation of metrics on an
orbifold quotient of a nilmanifold. Each orbifold in the deformation
contains singular points with order two isotropy. Isospectrality is
obtained by modifying a generalization of Sunada's theorem due to
DeTurck and Gordon.
Keywords:spectral geometry, global Riemannian geometry, orbifold, nilmanifold Categories:58J53, 53C20 |
15. CMB 2010 (vol 53 pp. 564)
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On $6$-Dimensional Nearly Kähler Manifolds In this paper we give a sufficient condition for a complete, simply connected, and strict nearly Kähler manifold of dimension 6 to be a homogeneous nearly Kähler manifold. This result was announced in a previous paper by the first author.
Keywords:Nearly Kähler manifold, 6-dimension, Homogeneous, The 1st Chern Class, Einstein manifolds Categories:53C40, 53C15 |
16. CMB 2010 (vol 53 pp. 438)
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Near-Homeomorphisms of Nöbeling Manifolds We characterize maps between $n$-dimensional Nöbeling manifolds that can be approximated by homeomorphisms.
Keywords:n-dimensional Nöbeling manifold, Z-set unknotting, near-homeomorphism Categories:55M10, 54F45 |
17. CMB 2010 (vol 53 pp. 412)
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Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field.
Keywords:Lorentz manifolds, curvature homogeneity, Einstein-like metrics Categories:53C50, 53C20, 53C30 |
18. CMB 2009 (vol 53 pp. 206)
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Semi-Slant Submanifolds of an Almost Paracontact Metric Manifold In this paper, we define and study the geometry of semi-slant submanifolds of an almost paracontact metric manifold. We give some characterizations for a submanifold to be semi-slant submanifold to be semi-slant product and obtain integrability conditions for the distributions involved in the definition of a semi-slant submanifold.
Keywords:paracontact metric manifold, slant distribution, semi-slant submanifold, semi-slant product Categories:53C15, 53C25, 53C40 |
19. CMB 2009 (vol 53 pp. 122)
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A Class of Finsler Metrics with Bounded Cartan Torsion In this paper, we find a class of $(\alpha,\beta)$ metrics which have a bounded Cartan torsion. This class contains all Randers metrics. Furthermore, we give some applications and obtain two corollaries about curvature of this metrics.
Keywords:Finsler manifold, $(\alpha,\beta)$ metric, Cartan torsion, R-quadratic, flag curvature Category:58E20 |
20. CMB 2009 (vol 52 pp. 257)
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Essential Surfaces in Graph Link Exteriors An irreducible graph manifold $M$ contains an essential torus if
it is not a special Seifert manifold.
Whether $M$ contains a closed essential surface of
negative Euler characteristic or not
depends on the difference of Seifert fibrations from the two sides
of a torus system which splits $M$ into Seifert manifolds.
However,
it is not easy to characterize geometrically the class of
irreducible graph manifolds which contain such surfaces.
This article studies this problem in the case of graph link exteriors.
Keywords:Graph link, Graph manifold, Seifert manifold, Essential surface Category:57M25 |
21. CMB 2009 (vol 52 pp. 18)
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Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds In this paper we study holomorphic maps between almost Hermitian
manifolds. We obtain a new criterion for the harmonicity of such
holomorphic maps, and we deduce some applications to horizontally
conformal holomorphic submersions.
Keywords:almost Hermitian manifolds, harmonic maps, harmonic morphism Categories:53C15, 58E20 |
22. CMB 2008 (vol 51 pp. 508)
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A Result in Surgery Theory We study the topological $4$-dimensional surgery problem
for a closed connected orientable
topological $4$-manifold $X$ with vanishing
second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has
one end and $F(r)$ is the free group of rank $r\ge 1$.
Our result is related to a theorem of Krushkal and Lee, and
depends on the validity of the Novikov conjecture for
such fundamental groups.
Keywords:four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map Categories:57N65, 57R67, 57Q10 |
23. CMB 2008 (vol 51 pp. 448)
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Stability of Biharmonic Legendrian Submanifolds in Sasakian Space Forms Biharmonic maps are defined as critical points of the bienergy.
Every harmonic map is a stable biharmonic map.
In this article, the stability of nonharmonic
biharmonic Legendrian submanifolds in Sasakian space forms is discussed.
Keywords:biharmonic maps, Sasakian manifolds, Legendrian submanifolds Categories:53C42, 53C40 |
24. CMB 2007 (vol 50 pp. 474)
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On Willmore's Inequality for Submanifolds Let $M$ be an $m$ dimensional submanifold in the Euclidean space
${\mathbf R}^n$ and $H$ be the mean curvature of $M$. We obtain
some low geometric estimates of the total square mean curvature
$\int_M H^2 d\sigma$. The low bounds are geometric invariants
involving the volume of $M$, the total scalar curvature of $M$,
the Euler characteristic and the circumscribed ball of $M$.
Keywords:submanifold, mean curvature, kinematic formul, scalar curvature Categories:52A22, 53C65, 51C16 |
25. CMB 2007 (vol 50 pp. 113)
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Hermitian Harmonic Maps into Convex Balls In this paper, we consider Hermitian harmonic maps from
Hermitian manifolds into convex balls. We prove that there exist
no non-trivial Hermitian harmonic maps from closed Hermitian
manifolds into convex balls, and we use the heat flow method to
solve the Dirichlet problem for Hermitian harmonic maps when the
domain is a compact Hermitian manifold with non-empty boundary.
Keywords:Hermitian harmonic map, Hermitian manifold, convex ball Categories:58E15, 53C07 |
