Results 31 to 40 of about 1,305 (80)
Constant scalar curvature metrics on connected sums
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 7, Page 405-450, 2003., 2003 The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension n ≥ 3, which minimizes the total scalar curvature on this conformal class. Let (M′, g′) and (M″, g″) be compact Riemannian n‐manifolds. We form their connected sumM′#M″ by
Dominic Joyce
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Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds
Analysis and Geometry in Metric Spaces, 2019 We show that if a CD(K, n) space (X, d, f ℋn) with n ≥ 2 has curvature bounded above by κ in the sense of Alexandrov then f is constant.
Kapovitch Vitali, Ketterer Christian
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Super parallel immersions in Euclidean space
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 1, Page 1-5, 2002., 2002 Two submanifolds of Euclidean n‐space En are called super parallel if the affine normal spaces are homothetic at the corresponding points. Characterizations are given for the action of conformal transformation on super parallel mates. Our notion is generalized to super transnormal submanifolds and its relation with super self‐parallel submanifolds and ...
Tarek Fathy Mersal +1 more
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An introduction to spherical orbit spaces
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 8, Page 453-469, 2002., 2002 Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. Two‐dimensional quotient spaces of the type Sn/G have been investigated extensively. This paper provides an elementary introduction, for nonspecialists, to this important field by way of several classical examples and supplies an explicit list of all the isotropy
Jill Mcgowan, Catherine Searle
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 We present some estimate of the Laplacian Spectrum and of Topological Invariants for Riemannian manifold with pinched sectional curvature and with non-empty and non-convex boundary with finite injectivity radius. These estimates do not depend directly on
Sabatini Luca
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Global pinching theorems of submanifolds in spheres
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 183-191, 2002., 2002 Let M be a compact embedded submanifold with parallel mean curvature vector and positive Ricci curvature in the unit sphere S n+p(n ≥ 2 , p ≥ 1). By using the Sobolev inequalities of P. Li (1980) to Lp estimate for the square length σ of the second fundamental form and the norm of a tensor Φ, related to the second fundamental form, we set up some ...
Kairen Cai
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Estimates on the first two buckling eigenvalues on spherical domains
, 2009 In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].Comment: This ...
Ashbaugh +8 more
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On hypersurfaces in a locally affine Riemannian Banach manifold
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 6, Page 375-379, 2002., 2002 We prove that an essential hypersurface of second order in an infinite dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature.
El-Said R. Lashin, Tarek F. Mersal
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Quaternion CR‐submanifolds of a quaternion Kaehler manifold
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 1, Page 27-37, 2001., 2001 We study the quaternion CR‐submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR‐submanifold.
Bassil J. Papantoniou, M. Hasan Shahid
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On the topology of manifolds with positive isotropic curvature
, 2008 We show that a closed orientable Riemannian $n$-manifold, $n \ge 5$, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of $S^{n-1} \times S^1$.Comment: 5 Pages. To appear in Proc.
Gadgil, Siddartha, Seshadri, Harish
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