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Homotopy type of manifolds with partially horoconvex boundary

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

    Let M be an n-dimensional compact connected manifold with boundary, κ>0 a constant and 1qn1 an integer. We prove that M supports a Riemannian metric with the interior q-curvature Kqqκ2 and the boundary q-curvature Λqqκ, if and only if M has the homotopy type of a CW complex with a finite number of cells with dimension (q1). Moreover, any Riemannian manifold M with sectional curvature Kκ2 and boundary principal curvature Λκ is diffeomorphic to the standard closed n-ball.

    AMSC: 53C20, 53C21