Riemannian manifolds
On the structure of Riemannian manifolds of almost nonnegative Ricci curvature
... due to Cheeger and Colding, which is crucially used in the proofs of our results. This theorem, conjectured originally by Gromov, says that the fundamental groups of a class of Riemannian manifolds with ...
6
Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds
... compact manifolds can be found in ...in Riemannian geometry, where nilpotent approximations are isometric to the Euclidean ...sub-Riemannian manifolds nilpotent approximations at different ...
38
On Convexity in Product of Riemannian Manifolds
... (resp. focal) points under their own metrics and connections. In [3], there are some interest- ing results in product of two C ∞ complete, simple connected smooth Riemannian manifolds without conjugate ...
7
Copulae on products of compact Riemannian manifolds
... compact Riemannian manifolds that has uniform ...homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact ...
16
Index of Quasiconformally Symmetric Semi Riemannian Manifolds
... semi-Riemannian manifolds with respect to any metric ...semi- Riemannian manifold and give the definition and some examples of the Ricci symmetric metric connections ...
15
Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound
... closed Riemannian manifolds due to Gromov and Buser, and give an alternative unified approach to these ...on Riemannian manifolds, showing, for example, that for geodesically convex compact ...
20
Gradient estimates for the Fisher–KPP equation on Riemannian manifolds
... Recently, Cao et al. [1] derived differential Harnack estimates for positive solutions to (1.1) on Riemannian manifolds with nonnegative Ricci curvature. The idea comes from [7, 8] where a systematic method ...
12
On the geometry of Riemannian manifolds with a Lie structure at infinity
... studying manifolds with a Lie structure at infin- ity comes from analysis, this class of manifolds leads to some interesting questions about their geometry, and this paper (the first one in a series of papers ...
33
Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds
... The connection between quadratic estimates and the existence of a bounded holo- morphic functional calculus of an operator provides a framework for applying har- monic analysis to the theory of differential operators. ...
134
3.Sobolev-type inequalities and complete Riemannian manifolds with nonnegative Ricci curvature
... n-dimensional Riemannian manifold M is isometric to R n if M satisfies the Nash ineqaulity ...on Riemannian manifolds satisfying the Nash ...such manifolds have maximal volume growth where the ...
11
On a class of contact Riemannian manifolds
... R(X,Y )ξ = κ η(Y )X − η(X)Y +µ η(Y )hX −η(X)hY , (1.1) where κ,µ are constant and 2h is the Lie derivative of φ in the direction ξ. It is remarkable that this class of spaces is invariant under D-homothetic deformations ...
8
The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning
... curved Riemannian manifolds by providing a comprehensive mathematical framework that formulates the coding/aggregation problem into an elegant ...where Riemannian optimization techniques become ...
130
Geodesic r preinvex functions on Riemannian manifolds
... On the other hand, in the last few years, several important concepts of non-linear anal- ysis and optimization problems have been extended from Euclidean space to a Rieman- nian manifolds. In general, a manifold ...
11
Harmonic Maps and Bi Harmonic Maps on CR Manifolds and Foliated Riemannian Manifolds
... Next, let us consider the analogue of harmonic maps and biharmonic maps for folia- tions are also given as follows. Transversally biharmonic maps between two foliated Riemannian manifolds were introduced by ...
18
Heterogeneous Riemannian Manifolds
... neighborhoods of two distinct points of M, contradicting the assumed heterogeneity of M. This verifies the hypothesis of Lemma 2.1 in 6, with the roles of M and M interchanged. Hence there exists an isometric immersion Φ ...
7
Volume growth and closed geodesics on Riemannian manifolds of hyperbolic type
... Theorem 1.2. Let (M ,g) be a compact Riemannian manifold of hyperbolic type without conjugate points and let X be its universal Riemannian covering. Then the growth function of the volume of geodesic ...
19
Harnack inequality for parabolic Lichnerowicz equations on complete noncompact Riemannian manifolds
... Theorem . (Song and Zhao []) Let M be a compact Riemannian manifold without boundary, Ric(M) ≥ . Let c(t) ∈ C (, ∞). Assume that u(x, t) is any positive solution of (.) on M with A(x) ≡ A, B(x) ≡ B, and ...
10
On Riemannian manifolds endowed with a locally conformal cosymplectic structure
... Let (M ,g) be an n-dimensional Riemannian manifold endowed with a metric tensor g. Let ΓTM and : TM → T ∗ M, Z → Z be the set of sections of the tangent bundle TM and the musical isomorphism defined by g , ...
8
The obstacle problem for conformal metrics on compact Riemannian manifolds
... Let (M n , g) be a compact Riemannian manifold of dimension n ≥ 3 with smooth boundary ∂M, M ¯ := M ∪ ∂M. In conformal geometry, it is interesting to find a complete metric g ˜ ∈ [g], the conformal class of g , ...
12
Closed conformal vector fields on pseudo Riemannian manifolds
... Let (M,g ) be a connected pseudo-Riemannian manifold of dimension n and signature (k, n − k) with 0 < k < n. Given a vector field W on M, we denote by W the one-form defined by W (X) = g(W,X). Then W is ...
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