Results 21 to 30 of about 1,124 (81)
High-order angles in almost-Riemannian geometry
, 2007 Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric ...
U. Boscain, M. Sigalotti
semanticscholar +1 more source
Homotheties and topology of tangent sphere bundles [PDF]
, 2014 We prove a Theorem on homotheties between two given tangent sphere bundles $S_rM$ of a Riemannian manifold $M,g$ of $\dim\geq 3$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced by the conformal class of $g$.
M.T.K. Abbassi +11 more
core +2 more sources
Universal inequalities for eigenvalues of quadratic polynomial operator of the Kohn Laplacian
, 2012 In this paper, we investigate the Dirichlet weighted eigenvalue problem of quadratic polynomial operator of the Kohn Laplacian on a bounded domain in the Heisenberg group Hn . We establish two inequalities for eigenvalues of this problem.
He-Jun Sun, Xuerong Qi
semanticscholar +1 more source
Weighted metrics on tangent sphere bundles [PDF]
, 2010 Natural metric structures on the tangent bundle and tangent sphere bundles $S_rM$ of a Riemannian manifold $M$ with radius function $r$ enclose many important unsolved problems. Admitting metric connections on $M$ with torsion, we deduce the equations of
Albuquerque, Rui
core +2 more sources
Geodetically convex sets in the Heisenberg group ${\mathbb H}^n$ [PDF]
arXiv, 2022 We classify the geodetically convex sets and geodetically convex functions on the Heisenberg group ${\mathbb H}^n$, $n\geq 1$.
arxiv
Pseudo-slant submanifolds in cosymplectic space forms
Acta Universitatis Sapientiae: Mathematica, 2016 In this paper, we study the geometry of the pseudo-slant submanifolds of a cosymplectic space form. Necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, pseudo-slant product, mixed geodesic and totally ...
Dirik Süleyman, Atçeken Mehmet
doaj +1 more source
A metric characterization of Carnot groups
, 2014 We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically ...
Donne, Enrico Le
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A note on sub-Riemannian structures associated with complex Hopf fibrations
, 2012 Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian structure and express them using the Riemannian curvature tensor of the Fubini-
Chang +8 more
core +1 more source
On Conditions for Unrectifiability of a Metric Space
Analysis and Geometry in Metric Spaces, 2014 We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a ...
Hajłasz Piotr, Malekzadeh Soheil
doaj +1 more source
Analysis and Geometry in Metric Spaces, 2013 In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0.
Capogna Luca +2 more
doaj +1 more source