Normal Split Submanifolds of Rational Homogeneous Spaces

Almost Extrinsically Homogeneous Submanifolds of Euclidean Space

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = TM ⊗ νM is equipped with an almost metric connection ∇̃ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂ − ∇̃ with the usual derivative ∂ in Rm is almost ∇̃-parallel. Then M admits an extrinsically homogeneous immersion into Rm.

Nonexistence of Stable Harmonic Maps to and from Certain Homogeneous Spaces and Submanifolds of Euclidean-Space

Call a compact Riemannian manifold M a strongly unstable manifold if it is not the range or domain of a nonconstant stable harmonic map and also the homotopy class of any map to or from M contains elements of arbitrarily small energy. If M is isometrically immersed in Euclidean space, then a condition on the second fundamental form of M is given which implies M is strongly unstable. As compact ...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Polyharmonic submanifolds in Euclidean spaces

B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces with constant mean curvature are minimal. M.S.C. 2010: 58E20, 53C43.