Deformations of Complete Submanifolds

2019 ◽  
pp. 453-475
Author(s):  
Marcos Dajczer ◽  
Ruy Tojeiro
Keyword(s):  
Complete Submanifolds

scholarly journals Complete submanifolds with relative nullity in space forms

2020 ◽  
Author(s):  
Samuel Canevari ◽  
Guilherme Machado de Freitas ◽  
Felippe Guimarães ◽  
Fernando Manfio ◽  
João Paulo dos Santos
Keyword(s):  
Space Forms ◽  
Relative Nullity ◽  
Complete Submanifolds

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).

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