Given a complex manifold X, a normal crossing divisor D ⊂ X whose irreducible components D 1 ,. .. , D s are smooth, and a choice of natural numbers r = (r 1 ,. .. , r s), we construct a manifold X(D, r) with an action of a torus Γ and we prove that some full subcategory of the category of Γ-equivariant vector bundles on X(D, r) is equivalent to the category of parabolic vector bundles on (X, D...

Recently, we have shown that there do not exist warped product semi-slant submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj Uddin, Balkan J. Geom. Appl. 13 (2008), 55–65]. The nearly cosymplectic structure generalizes the cosymplectic one. Therefore the nearly Kaehler structure generalizes the Kaehler structure in almost Hermitian setting. It is interesting that the warped ...

We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact be realized by a Hermitian manifold of constant scalar curvature and constant ⋆-scalar curvature which satisfies the Kaehler condition at the point in question.

In this paper, we study the partial convexity of smooth solutions to the heat equation on a compact or complete noncompact Riemannian manifold M or on Kaehler-Ricci flow. We show that under a natural assumption, a new partial convexity property for smooth solutions to the heat equation is preserved.

Another facet of geodesics is GAT or “geometric approximation theory”. It is very difficult to work directly with infinite dimensional geometry and GAT is a special method in projective K’́ahler geometry to make fiinite dimensional approximations of the infinite dimensional locally symmetric space Hω by genuine finite dimensional symmetric spaces of type GC/G with G = SU(N). The compact group SU...

We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold. 2000 Mathematics Subject Classification. 53C20, 53C21, 53C25.

In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to manifold. We study the geometry of foliations connection. Later, introduce base be local product

We show that generic rank conditions on the second fundamental form of an isometric immersion $f\colon M^{2n}\to\mathbb{R}^{2n+p}$ a Kaehler manifold complex dimension $n\geq 2$ into Euclidean space with low codimension $p$ implies submanifold has to be minimal. If $M^{2n}$ if simply connected, this amounts existence one-parameter associated family minimal immersions unless $f$ is holomorphic.