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Riemannian submanifolds with concircular canonical field

Bang-Yen Chen|Shihshu Walter Wei
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1525-1537|DOI 10.4134/BKMS.b181232

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참고문헌

키워드

concircular canonical fieldcanonical fieldconservative vector fieldconformal canonical field
주제분류수학

초록

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.

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.

참고문헌 (28)

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