On some real hypersurfaces of a complex projective space

Okumura, Masafumi

doi:10.1090/S0002-9947-1975-0377787-X

On some real hypersurfaces of a complex projective space
HTML articles powered by AMS MathViewer

by Masafumi Okumura PDF

Trans. Amer. Math. Soc. 212 (1975), 355-364 Request permission

Abstract:

A principal circle bundle over a real hypersurface of a complex projective space $C{P^n}$ can be regarded as a hypersurface of an odd-dimensional sphere. From this standpoint we can establish a method to translate conditions imposed on a hypersurface of $C{P^n}$ into those imposed on a hypersurface of ${S^{2n + 1}}$. Some fundamental relations between the second fundamental tensor of a hypersurface of $C{P^n}$ and that of a hypersurface of ${S^{2n + 1}}$ are given.

References

Shigeru Ishihara and Mariko Konishi, Differential geometry of fibred spaces, Publications of the Study Group of Geometry, Vol. 8, Kyoto University, Kyoto, 1973. MR 0405275
H. Blaine Lawson Jr., Rigidity theorems in rank-$1$ symmetric spaces, J. Differential Geometry 4 (1970), 349–357. MR 267492
Masafumi Okumura, Certain almost contact hypersurfaces in Kaehlerian manifolds of constant holomorphic sectional curvatures, Tohoku Math. J. (2) 16 (1964), 270–284. MR 176422, DOI 10.2748/tmj/1178243673
Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469. MR 200865
Patrick J. Ryan, Homogeneity and some curvature conditions for hypersurfaces, Tohoku Math. J. (2) 21 (1969), 363–388. MR 253243, DOI 10.2748/tmj/1178242949
Patrick J. Ryan, Hypersurfaces with parallel Ricci tensor, Osaka Math. J. 8 (1971), 251–259. MR 296859
Kentaro Yano and Shigeru Ishihara, Fibred spaces with invariant Riemannian metric, K\B{o}dai Math. Sem. Rep. 19 (1967), 317–360. MR 224028