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CR-submanifolds of a locally conformal Kaehler space form. (English) Zbl 0812.53017
Summary: The purpose of this paper is to continue the study of CR-submanifolds [A. Bejancu, Proc. Am. Math. Soc. 69, 135-142 (1978; Zbl 0376.53034) and Trans. Am. Math. Soc. 250, 333-345 (1979; Zbl 0401.53017)] and in particular of those of a locally conformal Kähler space form [K. Matsumoto, J. Korean Math. Soc. 21, 49-61 (1984; Zbl 0554.53039)]. Some results on the holomorphic sectional curvature, \(D\)- totally geodesic, \(D^ 1\)-totally geodesic and \(D^ 1\)-minimal CR- submanifolds of locally conformal Kaehler (l.c.k.)-space from \(\overline{M}(c)\) are obtained. We have also discussed the Ricci curvature as well as the scalar curvature of CR-submanifolds of \(\overline{M}(c)\).
53B25 Local submanifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
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