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 Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 3/4, Pages 446–455 (Mi jmag507)

On the vertical strong sphericity of Sasaki metric of tangent sphere bundles

A. L. Yampol'skii

Kharkiv State University

Abstract: The distribution $\mathcal L^q$ on the Riemannian manifold $M^n$ is called strong spherical if the curvature tensor of its metric satisfies the condition $R(X,Y)Z=k(\langle Y,Z\rangle X-\langle X,Z\rangle Y)$, ($k>0$) for any tangent to $M^n$ vectors $X$, $Z$ and any $Y\in\mathcal L^q$. The value $q=\operatorname{dim}\mathcal L^q$ is called the strong sphericity index. The conditions are considered at winch the vertical strong spherical distribution can exist on tangent sphere bundle $T_1M^n$ with Sasaki metric.

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Citation: A. L. Yampol'skii, “On the vertical strong sphericity of Sasaki metric of tangent sphere bundles”, Mat. Fiz. Anal. Geom., 3:3/4 (1996), 446–455

Citation in format AMSBIB
\Bibitem{Yam96} \by A.~L.~Yampol'skii \paper On the vertical strong sphericity of Sasaki metric of tangent sphere bundles \jour Mat. Fiz. Anal. Geom. \yr 1996 \vol 3 \issue 3/4 \pages 446--455 \mathnet{http://mi.mathnet.ru/jmag507}