Riemannian submersions and critical Riemannian metrics

Yosio MUTO

doi:10.2969/jmsj/02930493

Yosio MUTO

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JOURNAL FREE ACCESS

1977 Volume 29 Issue 3 Pages 493-511

DOI https://doi.org/10.2969/jmsj/02930493

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Published: 1977 Received: May 25, 1976 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] M. Berger, Quelques formules de variation pour une structure riemannienne, Ann. sci. Ecole Norm. Sup., 4^e serie, 3 (1970), 285-294.
[2] R. H. Escobales, Riemannian submersions with totally geodesic fibers, J. Differential Geometry, 10 (1975), 253-276.
[3] S. Ishihara, Vector fields in fibred spaces with invariant Riemannian metric, J. Differential Geometry, in honor of K. Yano, Kinokuniya, Tokyo, 1972, 163-178.
[4] S. Ishihara and M. Konishi, Differential geometry of fibred spaces, Publications of the study group of geometry, Tokyo, 8 (1973).
[5] Y. Muto, On some properties of a fibred Riemannian manifold, Sci. Rep. Yokohama Nat. Univ., Sect. I, No. 1 (1952), 1-14.
[6] Y. Muto, Curvature and critical Riemannian metrics, J. Math. Soc. Japan, 26 (1974), 686-697.
[7] Y. Muto, Critical Riemannian metrics, Tensor, 29 (1975), 125-133.
[8] T. Nagano, On fibred Riemannian manifolds, Sci. Papers College Gen. Ed. Univ. Tokyo, 10 (1960), 17-27.
[9] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J., 13 (1966), 459-469.
[10] S. Sasaki and Y. Hatakeyama, On differentiable manifolds with contact metric structures, J. Math. Soc. Japan, 14 (1962), 249-271.
[11] K. Yano and S. Ishihara, Differential geometry of fibred spaces, Kodai Math. Sem. Rep., 19 (1967), 257-288.
[12] K. Yano and S. Ishihara, Fibred spaces with invariant Riemannian metric, Kodai Math. Sem. Rep., 19 (1967), 317-360.

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