1,721,110 research outputs found

    Codazzi tensors on Sasakian manifolds

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    We prove that every compact Sasakian manifold of dimension 2n+1 whose horizon- tal sectional curvatures are non-negative and such that 2n is a simple eigenvalue of the Ricci operator admits no non-trivial Codazzi tensors. The same fact is true under suitable pinching assumptions on the φ-sectional curvatures

    On homogeneous η\eta -Einstein almost cosymplectic manifolds

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    We prove that every compact, homogeneous η-Einstein almost cosymplectic manifold is a cosymplectic manifold

    Non-existence of compact homogeneous PP-Sasakian manifolds

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    We show that there exist no compact homogeneous P-Sasakian manifolds whose structure vector field is invariant under the given Lie group action

    On locally homogeneous contact metric manifolds with Reeb flow invariant Jacobi operator

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    We show that a locally homogeneous, regular contact metric manifold, whose characteristic Jacobi operator is invariant under the Reeb flow, is not compact, provided it admits at least one negative ξ\xi-sectional curvature

    A note on Riemannian connections with skew torsion and the de Rham splitting

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    We prove that a Riemannian manifold admitting a metric connection with totally skew-symmetric torsion and reducible holonomy is locally reducible, provided it has nonpositive sectional curvature
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