<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with respect to which the unit tangent sphere bundle with induced g-natural metric is totally geodesic. Also, we equip the unit tangent sphere bundle T<sub>1</sub>M with g-natural contact (paracontact) metric structures, and we show that such structures are totally geodesic K-contact (K-paracontact) submanifolds of TM, if and only if the base manifold (M, g) has positive (negative) constant sectional curvature. Moreover, we establish a condition for g-natural almost contact B-metric structures on T1Msuch that these structures be totally geodesic submanifolds of TM.</p></abstract>

In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with respect to which the unit tangent sphere bundle with induced g-natural metric is totally geodesic. Also, we equip the unit tangent sphere bundle T1M with g-natural contact (paracontact) metric structures, and we show that such structures are totally geodesic K-contact (K-paracontact) submanifolds of TM, if and only if the base manifold (M, g) has positive (negative) constant sectional curvature. Moreover, we establish a condition for g-natural almost contact B-metric structures on T1Msuch that these structures be totally geodesic submanifolds of TM.

Totally geodesic property of the unit tangent sphere bundle with g-natural metrics

Department of Mathematics, Faculty of Science

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with...

Totally geodesic property of the unit tangent sphere bundle with g-natural metrics

Published Online: Sep 10, 2018

Page range: 152 - 166

Received: Apr 07, 2017

DOI: https://doi.org/10.2478/ausm-2018-0013

Keywords
natural metrics, sphere bundle, totally geodesic submanifold

© 2018 Esmaeil Peyghan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Totally geodesic property of the unit tangent sphere bundle with g-natural metrics

Published Online: Sep 10, 2018

Page range: 152 - 166

Received: Apr 07, 2017

DOI: https://doi.org/10.2478/ausm-2018-0013

Keywordsnatural metrics, sphere bundle, totally geodesic submanifold

© 2018 Esmaeil Peyghan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
natural metrics, sphere bundle, totally geodesic submanifold