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Homotopy type of manifolds with partially horoconvex boundary

    https://doi.org/10.1142/S0129167X1850074XCited by:0 (Source: Crossref)

    Let MM be an nn-dimensional compact connected manifold with boundary, κ>0κ>0 a constant and 1qn11qn1 an integer. We prove that MM supports a Riemannian metric with the interior qq-curvature Kqqκ2Kqqκ2 and the boundary qq-curvature ΛqqκΛqqκ, if and only if MM has the homotopy type of a CW complex with a finite number of cells with dimension (q1)(q1). Moreover, any Riemannian manifold MM with sectional curvature Kκ2Kκ2 and boundary principal curvature ΛκΛκ is diffeomorphic to the standard closed nn-ball.

    AMSC: 53C20, 53C21