Results 11 to 20 of about 1,004 (83)
A basic inequality for submanifolds in a cosymplectic space form [PDF]
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 9, Page 539-547, 2003., 2003 For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side.
Jeong-Sik Kim, Jaedong Choi
wiley +6 more sources
Minimal homogeneous submanifolds in euclidean spaces [PDF]
, 2002 We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally ...
Di Scala, Antonio Jose'
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Polar Actions on Berger Spheres [PDF]
, 2006 The object of this article is to study a torus action on a so-called Berger sphere. We also make some comments on polar actions on naturally reductive homogeneous spaces. Finally, we prove a rigidity-type theorem for Riemannian manifolds carrying a polar
ANTONIO J. DI SCALA +5 more
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On hypersurfaces in a locally affine Riemannian Banach manifold II
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 2, Page 99-104, 2004., 2004 In our previous work (2002), we proved that an essential second‐order hypersurface in an infinite‐dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine ...
El-Said R. Lashin, Tarek F. Mersal
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B.‐Y. Chen inequalities for semislant submanifolds in Sasakian space forms
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 27, Page 1731-1738, 2003., 2003 Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature. The notion of a semislant submanifold of a Sasakian manifold was introduced by J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez (1999).
Dragoş Cioroboiu
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A note on Chen′s basic equality for submanifolds in a Sasakian space form
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 11, Page 711-716, 2003., 2003 It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form M˜(c) of constant φ‐sectional curvature c < 1, with the structure vector field ξ tangent to M, satisfies Chen′s basic equality if and only if it is a 3‐dimensional minimal invariant submanifold.
Mukut Mani Tripathi +2 more
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Constant mean curvature hypersurfaces with constant δ‐invariant
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 67, Page 4205-4216, 2003., 2003 We completely classify constant mean curvature hypersurfaces (CMC) with constant δ‐invariant in the unit 4‐sphere S4 and in the Euclidean 4‐space 𝔼4.
Bang-Yen Chen, Oscar J. Garay
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Ricci curvature of submanifolds in Kenmotsu space forms
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 12, Page 719-726, 2002., 2002 In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al.
Kadri Arslan +4 more
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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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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
wiley +1 more source