scholarly journals Geometric realizations of generalized algebraic curvature operators

2009 ◽  
Vol 50 (1) ◽  
pp. 013515 ◽  
Author(s):  
P. Gilkey ◽  
S. Nikčević ◽  
D. Westerman
Keyword(s):  
Algebraic Curvature

scholarly journals A note on the structure of algebraic curvature tensors

2004 ◽  
Vol 382 ◽  
pp. 271-277 ◽  
Author(s):  
J.Carlos Dı́az-Ramos ◽  
Eduardo Garcı́a-Rı́o
Keyword(s):  
Algebraic Curvature ◽  
Curvature Tensors

scholarly journals On quasi-Clifford Osserman curvature tensors

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1241-1247
Author(s):  
Vladica Andrejic ◽  
Katarina Lukic
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Duality Principle ◽  
Algebraic Curvature ◽  
Curvature Tensors

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi- Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle.

scholarly journals Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yawei Chu ◽  
Dehe Li ◽  
Jundong Zhou
Keyword(s):  
Type Theorem ◽  
Ricci Soliton ◽  
Riemannian Curvature ◽  
Liouville Type ◽  
Curvature Condition ◽  
Liouville Type Theorem ◽  
Rigidity Results ◽  
Curvature Estimates ◽  
Finite Quotient ◽  
Algebraic Curvature

Let M n , g , f be a complete gradient shrinking Ricci soliton of dimension n ≥ 3 . In this paper, we study the rigidity of M n , g , f with pointwise pinching curvature and obtain some rigidity results. In particular, we prove that every n -dimensional gradient shrinking Ricci soliton M n , g , f is isometric to ℝ n or a finite quotient of S n under some pointwise pinching curvature condition. The arguments mainly rely on algebraic curvature estimates and several analysis tools on M n , g , f , such as the property of f -parabolic and a Liouville type theorem.

The Jordan normal form of Osserman algebraic curvature tensors

2001 ◽  
Vol 40 (1-4) ◽  
pp. 192-204 ◽  
Author(s):  
Peter Gilkey ◽  
Raina Ivanova
Keyword(s):  
Normal Form ◽  
Jordan Normal Form ◽  
Algebraic Curvature ◽  
Curvature Tensors
Sign in / Sign up

Export Citation Format

Share Document