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On the Lie derivative of symmetric connections. (English) Zbl 1383.53017

From the author’s introduction: The primary goal of our work is the extension of the operations of Lie derivative to objects defined on the vector-valued differential forms of manifold and to investigate some properties of the Lie derivative of the connection \(\nabla^\perp\) and the normal curvature tensor of the normal connectoin of the submanifold \(M\).
In Section 3, we introduce some properties of the normal connection on the submanifold \(M\) in \(\widetilde{M}\) by using the conjugate derivative with the normal connection for presenting the normal curvature of the submanifold \(M\) in \(\widetilde{M}\). In Section 4, we construct the Lie derivative of a linear connection on the Riemannnian manifold \(M\) and give some properties of the Lie derivative of the symmetric connection on \(M\).

MSC:

53B25 Local submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B05 Linear and affine connections
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