We study stability of non-compact gradient Kähler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kähler potential of the soliton will converge to the original soliton under Kähler-Ricci flow as time tends to infinity. To obtain this result, we construct appropriate ...

It is shown that the Hermitian-symmetric space CP1 × CP1 × CP1 and the flag manifold F1,2 endowed with any left invariant metric admit no compatible integrable almost complex structures (even locally) different from the invariant ones. As an application it is proved that any stable harmonic immersion from F1,2 equipped with an invariant metric into an irreducible Hermitian symmetric space of co...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

Computational conformal geometry focuses on developing the computational methodologies on discrete surfaces to discover conformal geometric invariants. In this work, we briefly summarize the recent developments for methods and related applications in computational conformal geometry. There are two major approaches, holomorphic differentials and curvature flow. Holomorphic differential method is...

Let M̄ be a complex space form of constant holomorphic sectional curvature c and let M be an n-dimensional CR-submanifold of (n− 1) CR-dimension in M̄. ThenM has an almost contact metric structure (F,U ,u,g) (see Section 2) induced from the canonical complex structure of M̄. Hence on an n-dimensional CR-submanifold of (n− 1) CRdimension, we can consider two structures, namely, almost contact struc...