Some properties of a cohomology group associated to a totally geodesic foliation

1986 ◽  
Vol 192 (3) ◽  
pp. 391-403 ◽  
Author(s):  
Grant Cairns
Keyword(s):  
Cohomology Group ◽  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Totally Geodesic Foliation

Semi-Riemannian hypersurfaces in $$\mathbb {L}^{n+1}$$ L n + 1 with a totally geodesic foliation of codimension one

2019 ◽  
Vol 110 (2) ◽  
Author(s):  
S. M. B. Kashani ◽  
M. J. Vanaei ◽  
S. M. Yaghoobi
Keyword(s):  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Codimension One ◽  
Totally Geodesic Foliation

scholarly journals The graph of a totally geodesic foliation

1995 ◽  
Vol 60 (3) ◽  
pp. 241-247 ◽  
Author(s):  
Robert Wolak
Keyword(s):  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Totally Geodesic Foliation

scholarly journals The weighted mixed curvature of a foliated manifold

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1097-1105
Author(s):  
Vladimir Rovenski
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Foliation ◽  
Foliated Manifold ◽  
Totally Geodesic ◽  
Geodesic Foliation ◽  
New Concepts ◽  
Sectional And Ricci Curvatures ◽  
Totally Geodesic Foliation ◽  
Foliated Riemannian Manifold

We introduce the weighted mixed curvature of an almost product (e.g. foliated) Riemannian manifold equipped with a vector field. We define several qth Ricci type curvatures, which interpolate between the weighed sectional and Ricci curvatures. New concepts of the ?mixed-curvature-dimension condition? and ?synthetic dimension of a distribution? allow us to renew the estimate of the diameter of a compact Riemannian foliation and splitting results for almost product manifolds of nonnegative/nonpositive weighted mixed scalar curvature. We also study the Toponogov?s type conjecture on dimension of a totally geodesic foliation with positive weighted mixed sectional curvature.

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

1983 ◽  
Vol 26 (3) ◽  
pp. 358-364 ◽  
Author(s):  
O. Gil-Medrano ◽  
A. M. Naveira
Keyword(s):  
Sectional Curvature ◽  
Euler Characteristic ◽  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Tensor Field ◽  
General Assumption ◽  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Characteristic Connection ◽  
Totally Geodesic Foliation

AbstractWith 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.

scholarly journals Curvature-dimension estimates for the Laplace–Beltrami operator of a totally geodesic foliation

2015 ◽  
Vol 126 ◽  
pp. 159-169 ◽  
Author(s):  
Fabrice Baudoin ◽  
Michel Bonnefont
Keyword(s):  
Beltrami Operator ◽  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Totally Geodesic Foliation

scholarly journals Euclidean hypersurfaces with a totally geodesic foliation of codimension one

2014 ◽  
Vol 176 (1) ◽  
pp. 215-224 ◽  
Author(s):  
M. Dajczer ◽  
V. Rovenski ◽  
R. Tojeiro
Keyword(s):  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Codimension One ◽  
Totally Geodesic Foliation

scholarly journals Hypersurfaces of space forms carrying a totally geodesic foliation

2019 ◽  
Vol 205 (1) ◽  
pp. 129-146
Author(s):  
Marcos Dajczer ◽  
Ruy Tojeiro
Keyword(s):  
Space Forms ◽  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Totally Geodesic Foliation

Laplacian on a totally geodesic foliation

1997 ◽  
Vol 60 (1-2) ◽  
pp. 74-79 ◽  
Author(s):  
Tae Ho Kang ◽  
Hong Kyung Pak ◽  
Jin Suk Pak
Keyword(s):  
Totally Geodesic ◽  
Geodesic Foliation ◽  
Totally Geodesic Foliation

An investigation on the existence of warped product irrotational screen-real lightlike submanifolds of metallic semi-Riemannian manifolds

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gauree Shanker ◽  
Ankit Yadav
Keyword(s):  
Riemannian Manifolds ◽  
Design Methodology ◽  
Warped Product ◽  
Sufficient Conditions ◽  
Totally Geodesic ◽  
Content Type ◽  
Lightlike Submanifolds ◽  
Totally Geodesic Foliation ◽  
Is Design ◽  
Lightlike Submanifold

PurposeThe purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.Design/methodology/approachThe paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.FindingsThe geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.Originality/valueAll results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

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