Complete homogeneous riemannian manifolds of negative sectional curvature

1975 ◽  
Vol 50 (1) ◽  
pp. 115-122 ◽  
Author(s):  
Su-Shing Chen
Keyword(s):  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds ◽  
Negative Sectional Curvature

scholarly journals Index theorems on manifolds with straight ends

2012 ◽  
Vol 148 (6) ◽  
pp. 1897-1968 ◽  
Author(s):  
Werner Ballmann ◽  
Jochen Brüning ◽  
Gilles Carron
Keyword(s):  
Sectional Curvature ◽  
Finite Volume ◽  
Riemannian Manifolds ◽  
Dirac Operators ◽  
Important Class ◽  
Index Theorems ◽  
Complete Riemannian Manifolds ◽  
Index Formulas ◽  
Negative Sectional Curvature

AbstractWe study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.

Prescribed k-Curvature Problems on Complete Noncompact Riemannian Manifolds

2018 ◽  
Vol 2020 (23) ◽  
pp. 9559-9592
Author(s):  
Jixiang Fu ◽  
Weimin Sheng ◽  
Lixia Yuan
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Ricci Tensor ◽  
Elliptic Partial Differential Equations ◽  
Nonlinear Elliptic ◽  
Noncompact Riemannian Manifolds ◽  
Curvature Tensors ◽  
Curvature Problem ◽  
Negative Sectional Curvature

Abstract To study the prescribed $k$-curvature problem of 2nd-order symmetric curvature tensors on complete noncompact Riemannian manifolds, we consider a class of fully nonlinear elliptic partial differential equations. It is proved that on a Riemannian manifold with negative sectional curvature and Ricci curvature bounded from below, the equation is solvable provided that all the eigenvalues of the tensor are negative. The result is applicable to the prescribed $k$-curvature problems of modified Schouten tensor and Bakry–Émery Ricci tensor.

Ball-homogeneous and disk-homogeneous Riemannian manifolds

1982 ◽  
Vol 180 (4) ◽  
pp. 429-444 ◽  
Author(s):  
Old?ich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

scholarly journals Cyclic homogeneous Riemannian manifolds

2015 ◽  
Vol 195 (5) ◽  
pp. 1619-1637 ◽  
Author(s):  
P. M. Gadea ◽  
J. C. González-Dávila ◽  
J. A. Oubiña
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

On δ-homogeneous Riemannian manifolds. II

2009 ◽  
Vol 50 (2) ◽  
pp. 214-222 ◽  
Author(s):  
V. N. Berestovskiĭ ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

scholarly journals On the Study of Jacobi Fields in Riemannian Manifolds

1970 ◽  
Vol 43 (4) ◽  
pp. 521-528
Author(s):  
Khondokar M Ahmed
Keyword(s):  
Field Equation ◽  
Key Words ◽  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Jacobi Equation ◽  
Standard Form ◽  
Jacobi Field ◽  
Jacobi Fields ◽  
New Approach

A new approach of finding a Jacobi field equation with the relation between curvature and geodesics of a Riemanian manifold M has been derived. Using this derivation we have made an attempt to find a standard form of this equation involving sectional curvature K and other related objects. Key words: Riemanign curvature, Sectional curvature, Jacobi equation, Jacobifield.    doi: 10.3329/bjsir.v43i4.2242 Bangladesh J. Sci. Ind. Res. 43(4), 521-528, 2008

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