1. CMB Online first
|Isometries and Hermitian Operators on Zygmund Spaces|
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.
Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries
Categories:46E15, 47B15, 47B38
2. CMB 2011 (vol 56 pp. 173)
|Semi-invariant Submersions from Almost Hermitian Manifolds|
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semi-invariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.
Keywords:Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion
3. CMB 2011 (vol 54 pp. 396)
|Parabolic Geodesics in Sasakian $3$-Manifolds|
We give explicit parametrizations for all parabolic geodesics in 3-dimensional Sasakian space forms.
Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds
4. CMB 2009 (vol 52 pp. 18)
|Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds |
In this paper we study holomorphic maps between almost Hermitian manifolds. We obtain a new criterion for the harmonicity of such holomorphic maps, and we deduce some applications to horizontally conformal holomorphic submersions.
Keywords:almost Hermitian manifolds, harmonic maps, harmonic morphism
5. CMB 2007 (vol 50 pp. 113)
|Hermitian Harmonic Maps into Convex Balls |
In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is a compact Hermitian manifold with non-empty boundary.
Keywords:Hermitian harmonic map, Hermitian manifold, convex ball
6. CMB 2004 (vol 47 pp. 73)
|Systems of Hermitian Quadratic Forms |
In this paper, we give some conditions to judge when a system of Hermitian quadratic forms has a real linear combination which is positive definite or positive semi-definite. We also study some related geometric and topological properties of the moduli space.
Keywords:hermitian quadratic form, positive definite, positive semi-definite