Generalized QR (GQR)- Lightlike Submanifolds of Indefinite Quaternion Kähler Manifolds

Article Sidebar

PDF
Published: Dec 15, 2021
Keywords:
Lightlike submanifolds; indefinite quaternion Kähler manifolds; QR-lightlike submanifolds, and SQR-lightlike submain-folds.

Main Article Content

Gauree Shanker
Department of Mathematics and Statistics Central University of Punjab, Bathinda, Punjab-151 401, India.
Ankit Yadav
Department of Mathematics and Statistics Central University of Punjab, Bathinda, Punjab-151 401, India.

Abstract

In this article, we introduce a new class of submanifolds namely GQR- lightlike submanifold of indefinite quaternion Kähler manifolds. It is observed that there is no inclusive relation between QR lightlike submanifolds and SQR lightlike submanifolds. We introduce a generalized submanifold, namely GQR-lightlike submanifold of indefinite quaternion Kähler manifold which contains QR lightlike submanifolds and SQR lightlike submanifolds. Further, we study various distributions of GQR- lightlike submanifolds and establish some important results.

Article Details

How to Cite
1.
Gauree Shanker, Ankit Yadav. Generalized QR (GQR)- Lightlike Submanifolds of Indefinite Quaternion Kähler Manifolds. J. Int. Acad. Phys. Sci. [Internet]. 2021 Dec. 15 [cited 2025 May 5];25(4):475-94. Available from: https://www.iaps.org.in/journal/index.php/journaliaps/article/view/894
Issue
Vol. 25 No. 4 (2021): Table of Content
Section
Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

References

K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Birkhäuser Verlag AG, Berlin, 2010.

M. Berger M., Sur les groupes d’holonomie homog’enes devarietees a connexion affine et. de varieteest riemanniennes, Bull. Soc. Math. Fr., 83 (1995), 279-330.

J. D. Perez, Indefinite quaternion space forms II, Ann. Stinnt. Univ. Al. I. Cuza Iasi. Sect. I Mat., 3 (1986), 63-68.

J. D. Perez and F. G. Santos, Indefinite quaternion space forms, Ann. Mat. Pura. Appl., 132 (1982), 383-398.

K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic, 1996.

A. I. Cătălin, Totally Umbilical Lightlike submanifolds, Bull. Math. Sc. Math. Roumanie, 37 (1996), 151-172

A. Duggal and D. H. Jin, Geometry of null curves, Math. J. Toyama Univ., 22 (1999), 95-120.