Expand all Collapse all | Results 26 - 50 of 75 |
26. CMB 2011 (vol 54 pp. 422)
Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space We classify real hypersurfaces in complex projective space whose
structure Jacobi operator satisfies two conditions at the same time.
Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditions Categories:53C15, 53B25 |
27. CMB 2010 (vol 53 pp. 684)
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 |
28. CMB 2010 (vol 53 pp. 564)
On $6$-Dimensional Nearly KÃ¤hler Manifolds In this paper we give a sufficient condition for a complete, simply connected, and strict nearly KÃ¤hler manifold of dimension 6 to be a homogeneous nearly KÃ¤hler manifold. This result was announced in a previous paper by the first author.
Keywords:Nearly KÃ¤hler manifold, 6-dimension, Homogeneous, The 1st Chern Class, Einstein manifolds Categories:53C40, 53C15 |
29. CMB 2010 (vol 53 pp. 412)
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 |
30. CMB 2010 (vol 53 pp. 516)
Asymptotics of Perimeter-Minimizing Partitions We prove that the least perimeter $P(n)$ of a partition of a smooth, compact Riemannian surface into $n$ regions of equal area $A$ is asymptotic to $n/2$ times the perimeter of a planar regular hexagon of area $A$. Along the way, we derive tighter estimates for flat tori, Klein bottles, truncated cylinders, and MÃ¶bius bands.
Category:53C42 |
31. CMB 2009 (vol 53 pp. 206)
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 |
32. CMB 2009 (vol 52 pp. 18)
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 |
33. CMB 2009 (vol 52 pp. 132)
On Projectively Flat $(\alpha,\beta)$-metrics The solutions to Hilbert's Fourth Problem in the regular case
are projectively flat Finsler metrics. In this paper,
we consider the so-called $(\alpha,\beta)$-metrics defined by a
Riemannian metric $\alpha$ and a $1$-form $\beta$, and find a
necessary and sufficient condition for such metrics to be projectively
flat in dimension $n \geq 3$.
Categories:53B40, 53C60 |
34. CMB 2009 (vol 52 pp. 87)
Holomorphic 2-Forms and Vanishing Theorems for Gromov--Witten Invariants On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form
$\a$, there is an almost complex structure associated with $\a$. We
show how this implies vanishing theorems for the Gromov--Witten
invariants of $X$. This extends the approach used by Parker and
the author for K\"{a}hler surfaces to higher dimensions.
Category:53D45 |
35. CMB 2008 (vol 51 pp. 467)
Coupled Vortex Equations on Complete KÃ¤hler Manifolds In this paper, we first investigate the Dirichlet
problem for coupled vortex equations. Secondly, we give existence
results for solutions of the coupled vortex equations on a class
of complete noncompact K\"ahler manifolds which include
simply-connected strictly negative curved manifolds, Hermitian
symmetric spaces of noncompact type and strictly pseudo-convex
domains equipped with the Bergmann metric.
Categories:58J05, 53C07 |
36. CMB 2008 (vol 51 pp. 448)
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 |
37. CMB 2008 (vol 51 pp. 359)
Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator Real hypersurfaces in a complex space form whose structure
Jacobi operator is symmetric along the Reeb flow are studied. Among
them, homogeneous real hypersurfaces of type $(A)$ in a complex
projective or hyperbolic space are characterized as those whose structure
Jacobi operator commutes with the shape operator.
Keywords:complex space form, real hypersurface, structure Jacobi operator Categories:53B20, 53C15, 53C25 |
38. CMB 2007 (vol 50 pp. 474)
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 |
39. CMB 2007 (vol 50 pp. 321)
On Lagrangian Catenoids Recently I. Castro and F. Urbano introduced the
Lagrangian catenoid.
Topologically, it is $\mathbb R\times S^{n-1}$ and its induced metric is
conformally flat,
but not cylindrical. Their result is that if a Lagrangian minimal
submanifold in
${\mathbb C}^n$ is foliated by round $(n-1)$-spheres, it is congruent to
a Lagrangian
catenoid. Here we study the question of conformally flat, minimal, Lagrangian
submanifolds in
${\mathbb C}^n$. The general problem is formidable, but we first show that such a
submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an
eigenvalue of multiplicity one. Then, restricting to the case of at most two
eigenvalues, we show that the submanifold is either flat and totally
geodesic or is
homothetic to (a piece of) the Lagrangian catenoid.
Categories:53C42, 53D12 |
40. CMB 2007 (vol 50 pp. 347)
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is of Codazzi Type We prove the non existence of real hypersurfaces in complex projective
space whose structure Jacobi operator is of Codazzi type.
Categories:53C15, 53B25 |
41. CMB 2007 (vol 50 pp. 365)
Equivariant Cohomology of $S^{1}$-Actions on $4$-Manifolds Let $M$ be a symplectic $4$-dimensional manifold equipped with a
Hamiltonian circle action with isolated fixed points. We describe a
method for computing its integral equivariant cohomology in terms of
fixed point data. We give some examples of these computations.
Categories:53D20, 55N91, 57S15 |
42. CMB 2007 (vol 50 pp. 113)
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 |
43. CMB 2007 (vol 50 pp. 97)
Characterizations of Real Hypersurfaces in a Complex Space Form We study a real hypersurface $M$ in a complex space
form $\mn$, $c \neq 0$, whose shape operator and structure tensor
commute each other on the holomorphic distribution of $M$.
Categories:53C40, 53C15 |
44. CMB 2007 (vol 50 pp. 24)
Invariant Metrics with Nonnegative Curvature on Compact Lie Groups We classify the left-invariant metrics with nonnegative sectional curvature on $\SO(3)$ and $U(2)$.
Category:53C20 |
45. CMB 2006 (vol 49 pp. 321)
Polygons with Prescribed Gauss Map in Hadamard Spaces and Euclidean Buildings We show that given a stable weighted configuration on the asymptotic
boundary of a
locally compact Hadamard space, there is a polygon with Gauss
map prescribed by the given weighted configuration.
Moreover, the same result holds for
semistable configurations on arbitrary Euclidean buildings.
Keywords:Euclidean buildings, Hadamard spaces, polygons Category:53C20 |
46. CMB 2006 (vol 49 pp. 226)
The Spectrum and Isometric Embeddings of Surfaces of Revolution A sharp upper bound on the first $S^{1}$ invariant eigenvalue of the Laplacian
for $S^1$ invariant metrics on $S^2$ is used to find obstructions to the existence
of $S^1$ equivariant isometric embeddings of such metrics in $(\R^3,\can)$. As a
corollary we prove: If the first four distinct eigenvalues have even multiplicities
then the metric cannot be equivariantly, isometrically embedded in $(\R^3,\can)$. This
leads to generalizations of some classical results in the theory of surfaces.
Categories:58J50, 58J53, 53C20, 35P15 |
47. CMB 2006 (vol 49 pp. 134)
Real Hypersurfaces in Complex Two-Plane Grassmannians with Vanishing Lie Derivative In this paper we give a characterization of real hypersurfaces of type $A$ in a complex
two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ which are tubes over totally geodesic
$G_2(\mathbb{C}^{m+1})$ in $G_2(\mathbb{C}^{m+2})$ in terms of the {\it vanishing Lie
derivative\/} of the shape operator $A$ along the direction of the Reeb vector field $\xi$.
Categories:53C40, 53C15 |
48. CMB 2006 (vol 49 pp. 152)
Comparison Geometry With\\$L^1$-Norms of Ricci Curvature We investigate the geometry of manifolds with bounded Ricci
curvature in $L^1$-sense. In particular, we generalize the
classical volume comparison theorem to our situation and obtain a
generalized sphere theorem.
Keywords:Mean curvature, Ricci curvature Category:53C20 |
49. CMB 2006 (vol 49 pp. 36)
Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles Using a modification of Webster's proof of the Newlander--Nirenberg
theorem, it is shown that, for a weakly convergent sequence of
integrable unitary connections on a complex vector bundle over a
complex manifold, there is a subsequence of local holomorphic frames
that converges strongly in an appropriate Holder class.
Categories:57M50, 58E20, 53C24 |
50. CMB 2005 (vol 48 pp. 561)
A Note on Lagrangian Loci of Quotients We study Hamiltonian actions of compact groups in the presence of
compatible involutions. We show that the Lagrangian fixed point set
on the symplectically reduced space is isomorphic to the disjoint
union of the involutively reduced spaces corresponding to
involutions on the group strongly inner to the given one.
Our techniques imply that the solution to the eigenvalues of a sum problem
for a given real form can be reduced to the quasi-split real form in the
same inner class. We also consider invariant quotients with respect to
the corresponding real form of the complexified group.
Keywords:Quotients, involutions, real forms, Lagrangian loci Category:53D20 |