Normal and Integral Currents

1960 ◽  
Vol 72 (3) ◽  
pp. 458 ◽  
Author(s):  
Herbert Federer ◽  
Wendell H. Fleming
Keyword(s):  
Integral Currents

Stokes' Theorem for Integral Currents Modulo ν

1977 ◽  
Vol 99 (2) ◽  
pp. 379
Author(s):  
Sandra O. Paur
Keyword(s):  
Integral Currents

scholarly journals Homology Groups in Warped Product Submanifolds in Hyperbolic Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yanlin Li ◽  
Akram Ali ◽  
Fatemah Mofarreh ◽  
Nadia Alluhaibi
Keyword(s):  
Fundamental Group ◽  
Hyperbolic Space ◽  
Ricci Curvature ◽  
Warped Product ◽  
Hyperbolic Spaces ◽  
Warping Function ◽  
Base Manifold ◽  
Homology Groups ◽  
Minimal Base ◽  
Integral Currents

In this paper, we show that if the Laplacian and gradient of the warping function of a compact warped product submanifold Ω p + q in the hyperbolic space ℍ m − 1 satisfy various extrinsic restrictions, then Ω p + q has no stable integral currents, and its homology groups are trivial. Also, we prove that the fundamental group π 1 Ω p + q is trivial. The restrictions are also extended to the eigenvalues of the warped function, the integral Ricci curvature, and the Hessian tensor. The results obtained in the present paper can be considered as generalizations of the Fu–Xu theorem in the framework of the compact warped product submanifold which has the minimal base manifold in the corresponding ambient manifolds.

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