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Sasakian manifold with pseudo-Riemannian metric by Takahashi, Toshio is a Mathematics article available to read on EtoBox.

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Introduction. Sasakian manifold with Riemannian metric is defined by S. Sasaki [5]. In this paper, we want to define Sasakian manifold with pseudo-Riemannian metric, and discuss the classification of Sasakian manifolds. In section 1, we define a Sasakian manifold (with pseudo-Riemannian metric). In section 2, we define the model spaces of Sasakian manifolds which are used in section 4 for the classification of Sasakian manifolds of constant φ-sectional curvatures. In section 3, we discuss Z)-homothetic deformation which is defined by S. Tanno [9], and prove some fundamental lemmas concerning completeness of the deformed metric. In section 5, we prove that a Sasakian manifold, satisfying R(X, Y) R = 0 for all tangent vectors X and Y, is of constant curvature. In section 6, we discuss a Sasakian manifold M^n +1 which is properly and isometrically immersed in £f n+2 .

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Author

Takahashi, Toshio

Publisher

Mathematical Institute of Tohoku University; Mathematical Institute, Tohoku University; Tohoku University (ISSN 0040-8735)

Published

1969

Language

EN

Field

Mathematics (Physical Sciences)