2012
DOI: 10.7546/jgsp-17-2010-87-102
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Properties of Biharmonic Submanifolds in Spheres

Abstract: Abstract. In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature submanifolds in spheres.

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Cited by 5 publications
(8 citation statements)
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References 26 publications
(30 reference statements)
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“…From (2) we see that CMC surfaces, i.e. surfaces with constant mean curvature, in space forms are biconservative.…”
Section: Introductionmentioning
confidence: 94%
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“…From (2) we see that CMC surfaces, i.e. surfaces with constant mean curvature, in space forms are biconservative.…”
Section: Introductionmentioning
confidence: 94%
“…In general, a submanifold is called biconservative if div S 2 = 0. Moreover, the class of biconservative submanifolds includes that of biharmonic submanifolds, which have been of large interest in the last decade (see, for example, [1,2,3,4,9,19,20]). Biharmonic submanifolds are characterized by the vanishing of the bitension field and they represent a generalization of harmonic (minimal) submanifolds.…”
Section: Introductionmentioning
confidence: 99%
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“…When x 0 = 0, the submanifold is called mass-symmetric (see [13]). It was proved in [8,9] that, in general, a proper-biharmonic compact constant mean curvature submanifold M m of S n is either a 1-type submanifold of R n+1 with center of mass of norm equal to 1 √ 2 , or is a mass-symmetric 2-type submanifold of R n+1 . Now, using Theorem 3.5 in [4], where all mass-symmetric 2-type integral surfaces in S 5 (1) were determined, and Proposition 4.1 in [11], the result in [31] can be (partially) reobtained.…”
Section: An Anti-invariant Riemannian Immersion and Is Properbiharmomentioning
confidence: 99%