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Results 1 - 25 of 72 |
1. CMB Online first
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Curvature of $K$-contact Semi-Riemannian Manifolds In this paper we characterize $K$-contact semi-Riemannian manifolds
and Sasakian semi-Riemannian manifolds in terms of
curvature. Moreover, we show that any conformally flat $K$-contact
semi-Riemannian manifold is Sasakian and of constant sectional
curvature $\kappa=\varepsilon$, where $\varepsilon =\pm 1$ denotes
the causal character of the Reeb vector field. Finally, we give some
results about the curvature of a $K$-contact Lorentzian manifold.
Keywords:contact semi-Riemannian structures, $K$-contact structures, conformally flat manifolds, Einstein Lorentzian-Sasaki manifolds Categories:53C50, 53C25, 53B30 |
2. 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 |
3. 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 |
4. 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 |
5. CMB 2011 (vol 56 pp. 306)
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Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel We prove the non-existence of real hypersurfaces in complex projective
space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and
satisfies a further condition.
Keywords:complex projective space, real hypersurface, structure Jacobi operator Categories:53C15, 53C40 |
6. CMB 2011 (vol 56 pp. 184)
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On Some Non-Riemannian Quantities in Finsler Geometry In this paper we study several non-Riemannian quantities in Finsler
geometry. These non-Riemannian quantities play an important role in
understanding the geometric properties of Finsler metrics. In
particular, we study a new non-Riemannian quantity defined by the
S-curvature. We show some relationships among the flag curvature,
the S-curvature, and the new non-Riemannian quantity.
Keywords:Finsler metric, S-curvature, non-Riemannian quantity Categories:53C60, 53B40 |
7. CMB Online first
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Randers Metrics of Constant Scalar Curvature Randers metrics are a special class of Finsler metrics. Every Randers
metric can be expressed in terms of a Riemannian metric and a vector
field via Zermelo navigation.
In this paper, we show that a Randers metric has constant scalar
curvature if the Riemannian metric has constant scalar curvature and
the vector field is homothetic.
Keywords:Randers metrics, scalar curvature, S-curvature Categories:53C60, 53B40 |
8. CMB 2011 (vol 56 pp. 127)
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Evolution of Eigenvalues along Rescaled Ricci Flow In this paper, we discuss monotonicity formulae of various entropy functionals under various
rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue
of a family of geometric operators $-4\Delta + kR$ is monotonic along the
normalized Ricci flow for all $k\ge 1$ provided the initial manifold has
nonpositive total scalar curvature.
Keywords:monotonicity formulas, Ricci flow Categories:58C40, 53C44 |
9. CMB 2011 (vol 55 pp. 870)
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Left Invariant Einstein-Randers Metrics on Compact Lie Groups In this paper we study left invariant Einstein-Randers metrics on compact Lie
groups. First, we give a method to construct left invariant non-Riemannian Einstein-Randers metrics
on a compact Lie group, using the Zermelo navigation data.
Then we prove that this gives a complete classification of left invariant Einstein-Randers metrics on compact simple
Lie groups with the underlying Riemannian metric naturally reductive.
Further, we completely determine the identity component of the group of
isometries for this type of metrics on simple groups. Finally, we study some
geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature
of such metrics.
Keywords:Einstein-Randers metric, compact Lie groups, geodesic, flag curvature Categories:17B20, 22E46, 53C12 |
10. 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 |
11. 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 |
12. CMB 2011 (vol 56 pp. 116)
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Central Extensions of Loop Groups and Obstruction to Pre-Quantization An explicit construction of a pre-quantum line bundle for the moduli
space of flat $G$-bundles over a Riemann surface is given, where $G$
is any non-simply connected compact simple Lie group. This work helps
to explain a curious coincidence previously observed between
Toledano Laredo's work classifying central extensions of loop groups
$LG$ and the author's previous work on the obstruction to
pre-quantization of the moduli space of flat $G$-bundles.
Keywords:loop group, central extension, prequantization Categories:53D, 22E |
13. CMB 2011 (vol 56 pp. 44)
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Polystable Parabolic Principal $G$-Bundles and Hermitian-Einstein Connections We show that there
is a bijective correspondence between the polystable parabolic
principal $G$-bundles and solutions of the Hermitian-Einstein
equation.
Keywords:ramified principal bundle, parabolic principal bundle, Hitchin-Kobayashi correspondence, polystability Categories:32L04, 53C07 |
14. CMB 2011 (vol 55 pp. 663)
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An Onofri-type Inequality on the Sphere with Two Conical Singularities In this paper, we give a new proof of the Onofri-type inequality
\begin{equation*}
\int_S e^{2u} \,ds^2 \leq 4\pi(\beta+1) \exp \biggl\{
\frac{1}{4\pi(\beta+1)} \int_S |\nabla u|^2 \,ds^2 +
\frac{1}{2\pi(\beta+1)} \int_S u \,ds^2 \biggr\}
\end{equation*}
on the sphere $S$ with Gaussian curvature $1$ and with conical
singularities divisor $\mathcal A = \beta\cdot p_1 + \beta \cdot p_2$ for
$\beta\in (-1,0)$; here $p_1$ and $p_2$ are antipodal.
Categories:53C21, 35J61, 53A30 |
15. CMB 2011 (vol 55 pp. 723)
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First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces We extend results proved by the second author (Amer. J. Math., 2009)
for nonnegatively curved Alexandrov spaces
to general compact Alexandrov spaces $X$ with curvature bounded
below.
The gradient flow of a geodesically convex functional on the quadratic Wasserstein
space $(\mathcal P(X),W_2)$ satisfies the evolution variational inequality.
Moreover, the gradient flow enjoys uniqueness and contractivity.
These results are obtained by proving a first variation formula for
the Wasserstein distance.
Keywords:Alexandrov spaces, Wasserstein spaces, first variation formula, gradient flow Categories:53C23, 28A35, 49Q20, 58A35 |
16. CMB 2011 (vol 55 pp. 611)
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Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection In this paper we prove Chen inequalities for submanifolds of real space
forms endowed with a semi-symmetric non-metric connection, i.e., relations
between the mean curvature associated with a semi-symmetric non-metric
connection, scalar and sectional curvatures, Ricci curvatures and the
sectional curvature of the ambient space. The equality cases are considered.
Keywords:real space form, semi-symmetric non-metric connection, Ricci curvature Categories:53C40, 53B05, 53B15 |
17. CMB 2011 (vol 55 pp. 108)
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On Segre Forms of Positive Vector Bundles The goal of this note is to prove that the signed Segre forms of Griffiths' positive vector bundles are
positive.
Categories:53C55, 32L05 |
18. CMB 2011 (vol 55 pp. 329)
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Non-Discrete Complex Hyperbolic Triangle Groups of Type $(n,n, \infty;k)$ A complex hyperbolic triangle group is a group
generated by three involutions fixing complex lines in complex
hyperbolic space. Our purpose in this paper is to improve a previous result
and to discuss discreteness of complex hyperbolic
triangle groups of type $(n,n,\infty;k)$.
Keywords:complex hyperbolic triangle group Categories:51M10, 32M15, 53C55, 53C35 |
19. CMB 2011 (vol 55 pp. 474)
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A Note on Randers Metrics of Scalar Flag Curvature Some families of Randers metrics of scalar flag curvature are
studied in this paper. Explicit examples that are neither locally
projectively flat nor of isotropic $S$-curvature are given. Certain
Randers metrics with Einstein $\alpha$ are considered and proved to
be complex. Three dimensional Randers manifolds, with $\alpha$
having constant scalar curvature, are studied.
Keywords:Randers metrics, scalar flag curvature Categories:53B40, 53C60 |
20. CMB 2011 (vol 55 pp. 138)
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Projectively Flat Fourth Root Finsler Metrics In this paper, we study locally projectively flat fourth root
Finsler metrics and their generalized metrics. We prove that if they
are irreducible, then they must be locally Minkowskian.
Keywords:projectively flat, Finsler metric, fourth root Finsler metric Category:53B40 |
21. CMB 2011 (vol 55 pp. 114)
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On Characterizations of Real Hypersurfaces in a Complex Space Form with $\eta$-Parallel Shape Operator In this paper we study real hypersurfaces in a non-flat complex space form with $\eta$-parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained.
Keywords:complex space form, Hopf hypersurfaces, ruled real hypersurfaces, $\eta$-parallel shape operator Categories:53C40, 53C15 |
22. 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 |
23. CMB 2011 (vol 54 pp. 422)
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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 |
24. 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 |
25. 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 |
