Sphere Theorems

2000 ◽  
pp. 865-903 ◽  
Author(s):  
Katsuhiro Shiohama
Keyword(s):  
Sphere Theorems

RIGIDITY AND SPHERE THEOREMS FOR SUBMANIFOLDS

1994 ◽  
Vol 48 (2) ◽  
pp. 291-306 ◽  
Author(s):  
Katsuhiro SHIOHAMA ◽  
Hongwei XU
Keyword(s):  
Sphere Theorems

scholarly journals The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven

2017 ◽  
Vol 7 (4) ◽  
pp. 1119-1170
Author(s):  
Stefan Ivanov ◽  
Alexander Petkov ◽  
Dimiter Vassilev
Keyword(s):  
Contact Manifold ◽  
Sphere Theorems

VANISHING AND TOPOLOGICAL SPHERE THEOREMS FOR SUBMANIFOLDS IN A HYPERBOLIC SPACE

2008 ◽  
Vol 19 (07) ◽  
pp. 811-822 ◽  
Author(s):  
HAIPING FU ◽  
HONGWEI XU
Keyword(s):  
Hyperbolic Space ◽  
Measure Theory ◽  
Geometric Measure Theory ◽  
Vanishing Theorem ◽  
Sphere Theorem ◽  
Homology Groups ◽  
Geometric Measure ◽  
Complete Submanifolds ◽  
Negative Constant ◽  
Sphere Theorems

We extend the vanishing and sphere theorems due to Lawson, Simons, Xin, Shiohama and Xu. By using the techniques of calculus of variations in the geometric measure theory, we prove the vanishing theorem for homology groups of submanifolds in the hyperbolic space Hn(c) with negative constant curvature c. Moreover, we obtain a topological sphere theorem for certain complete submanifolds in Hn(c).

Differentiable sphere theorems for Ricci curvature

1993 ◽  
Vol 214 (1) ◽  
pp. 245-259 ◽  
Author(s):  
Gregório Pacelli Bessa
Keyword(s):  
Ricci Curvature ◽  
Sphere Theorems
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