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The Gauss-Bonnet Integrand for a Class of Riemannian Manifolds Admitting Two Orthogonal Complementary Foliations

Published online by Cambridge University Press:  20 November 2018

O. Gil-Medrano  and
A. M. Naveira
O. Gil-Medrano
Affiliation:
Departamento De Geometría y TopologíA. Facultad De Ciencias Matemáticas Universidad De Valencia. Burjasot (Valencia), Spain
A. M. Naveira
Affiliation:
Departamento De Geometría y TopologíA. Facultad De Ciencias Matemáticas Universidad De Valencia. Burjasot (Valencia), Spain
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Abstract

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With the general assumption that the manifold admits two orthogonal complementary foliations, one of which is totally geodesic, we study the components of the curvature tensor field of the characteristic connection.

In the case where the manifold is compact, orientable of dimension 6 or 8 and the dimension of the totally geodesic foliation is 4, we relate the sign of the Euler characteristic of the manifold and that of the sectional curvature of the leaves of both foliations.

Keywords

53C1557R3057R20Almost-product structurecharacteristic connectiontotally geodesictotally umbilicalminimal foliationGauss-Bonnet integrand

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 358 - 364
Copyright
Copyright © Canadian Mathematical Society 1983

References

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