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Cheeger-Gromoll type metrics on the \((1,1)\)-tensor bundles. (English) Zbl 1302.53017

J. Contemp. Math. Anal., Armen. Acad. Sci. 48, No. 6, 247-258 (2013) and Izv. Nats. Akad. Nauk Armen., Mat. 48, No. 6, 59-70 (2013).
Summary: Using a Riemannian metric on a differentiable manifold, a Cheeger-Gromoll type metric is introduced on the \((1,1)\)-tensor bundle of the manifold. Then the Levi-Civita connection, Riemannian curvature tensor, Ricci tensor, scalar curvature and sectional curvature of this metric are calculated. Also, a para-Nordenian structure on the the \((1,1)\)-tensor bundle with this metric is constructed and the geometric properties of this structure are studied.

MSC:

53A45 Differential geometric aspects in vector and tensor analysis
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