Bang-Yen Chen

9 Questions 41 Answers 0 Followers

Questions related from Bang-Yen Chen

Is it true that every immersion of a complex projective n-space in a Euclidean m-space satisfies ∫ |H|^(2n) dV ≥ ((2(n+1)π/n)^n/π! ?

In the question given above, H is the mean curvature of the immersed complex projective space in the Euclidean m-space

30 January 2016 9,417 4 View

Is it true that every immersion of a quaternion projective n-space in a Euclidean m-space satisfies ∫ |H|^(4n) dV ≥ (2/((2n+1)!))((2n+3)π/n)^(2n) ?

In the question given above, H is the mean curvature of the immersed real projective space in the Euclidean m-space.

30 January 2016 4,514 4 View

Are there relationship between tension and energy of a non-constant map from a closed Riemannian manifold into another Riemannian manifold?

For a differential map ϕ from a closed Riemannian manifold M into another Riemannian manifold, the energy E(ϕ) of ϕ is defined as the integral ∫ |dϕ|2 *1, whee *1 is the volume element of M.

13 January 2016 5,283 1 View

Is it true that the only closed hypersurfaces of a Euclidean m-space with finite type Gauss map are hyperspheres?

The Gauss map µ of a hypersurface is said to be of finite type if the Gauss map µ is the spectral decomposition of µ is of finite sum, i.e., µ = µ1+...+µn, ∆µi = ciµi, for some integer n, where ci...

13 January 2016 6,715 0 View

Is it true that for every imbedding of an n-torus T^n in any Euclidean m-space satisfies ∫ |H|^n dV ≥ (4/n)^(n/2) π^n?

In my question given above, H is the mean curvature of the imbedded n-torus in the Euclidean m-space with arbitrary codimension.

07 January 2016 3,785 1 View

Is it true that every immersion of a real projective 2n-space in a Euclidean m-space satisfies ∫ |H|^(2n) dV ≥ ((2n+1)/n)^n c_{2n}/2 ?

In the question given above, H is the mean curvature of the immersed real projective space in the Euclidean m-space and c2n denotes the volume of the unit 2n-sphere.

07 January 2016 5,801 2 View

Do there exist non-mass-symmetric 2-type surfaces lying fully in a hypersphere of Euclidean 5-space?

A compact submanifold lying in a hypersphere Sm of a Euclidean (m+1)-space Em+1 is call mass-symmetric if the center of mass of M is the center of the hypersphere.

27 December 2015 9,624 1 View

What are the necessary and sufficient conditions for a Dupin hypersurface of a hypersphere to be of finite type?

A hypersurface is called a Dupin hypersurface if the multiplicities of its principal curvatures are constant and moreover each principal curvature isconstant along its principal directions.

27 December 2015 6,656 2 View

What are the relations between #_2(M) of a compact symmetric space M and the smallest number of cells needed to have a CW-complex structure on M?

For a compact symmetric space M, the 2-number #2(M) is the maximal possible cardinality of a subset A2(M) of M such that the point symmetry sx fixes every point of A2(M) for every x ∈ A2(M) (see...

17 December 2015 8,118 4 View