Hiroshima Mathematical Journal

On Riemannian foliations admitting transversal conformal fields

Woo Cheol Kim and Seoung Dal Jung

Full-text: Open access

Abstract

Let $(M,g_M, \mathscr F)$ be a closed, connected Riemannian manifold with a Riemannian foliation $\mathscr F$ of nonzero constant transversal scalar curvature. When $M$ admits a transversal nonisometric conformal field, we find some generalized conditions that $\mathscr F$ is transversally isometric to $(S^q(1/c),G)$, where $G$ is the discrete subgroup of $O(q)$ acting by isometries on the last $q$ coordinates of the sphere $S^q(1/c)$ of radius $1/c$.

Note

This paper was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2018R1A2B2002046).

Article information

Source
Hiroshima Math. J., Volume 50, Number 1 (2020), 59-72.

Dates
Received: 22 December 2018
Revised: 21 October 2019
First available in Project Euclid: 7 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1583550015

Digital Object Identifier
doi:10.32917/hmj/1583550015

Mathematical Reviews number (MathSciNet)
MR4074379

Zentralblatt MATH identifier
07197870

Subjects
Primary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]
Secondary: 57R30: Foliations; geometric theory

Keywords
Riemannian foliation transversal conformal field generalized Obata theorem

Citation

Kim, Woo Cheol; Jung, Seoung Dal. On Riemannian foliations admitting transversal conformal fields. Hiroshima Math. J. 50 (2020), no. 1, 59--72. doi:10.32917/hmj/1583550015. https://projecteuclid.org/euclid.hmj/1583550015


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