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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.
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참고문헌 (28)
참고문헌 신청
R. L. Bishop / 1969 / Manifolds of Negative Curvature / Transactions of the American Mathematical Society 145:1~49
B.-Y. Chen / 2011 / Pseudo-Riemannian Geometry, δ-Invariants and Applications / World Scienti fic Publishing Co. Pte. Ltd.
Bang-Yen Chen / 2014 / A simple characterization of generalized Robertson–Walker spacetimes / General Relativity and Gravitation 46(12):5
Bang-Yen Chen / 2015 / SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS / 대한수학회보 52(5):1535~1547
B.-Y. Chen / 2016 / Differential geometry of rectifying submanifolds / Int. Electron. J. Geom 9(2):1~8
B.-Y. Chen / 2011 / Pseudo-Riemannian Geometry, δ-Invariants and Applications / World Scienti fic Publishing Co. Pte. Ltd.
Bang-Yen Chen / 2014 / A simple characterization of generalized Robertson–Walker spacetimes / General Relativity and Gravitation 46(12):5
Bang-Yen Chen / 2015 / SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS / 대한수학회보 52(5):1535~1547
B.-Y. Chen / 2016 / Differential geometry of rectifying submanifolds / Int. Electron. J. Geom 9(2):1~8
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