Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(6): 1525-1537

Online first article August 6, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b181232

Copyright © The Korean Mathematical Society.

Riemannian submanifolds with concircular canonical field

Bang-Yen Chen, Shihshu Walter Wei

Michigan State University; University of Oklahoma

Abstract

Let $\tilde M$ be a Riemannian manifold equipped with a concircular vector field $\tilde X$ and $M$ a submanifold (with its induced metric) of $\tilde M$. Denote by $X$ the restriction of $\tilde X$ on $M$ and by $X^T$ the tangential component of $X$, called the canonical field of $M$. In this article we study submanifolds of $\tilde M$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.

Keywords: concircular canonical field, canonical field, conservative vector field, conformal canonical field

MSC numbers: 53C40, 53C42