Let X be a 2n−dimensional smooth manifold. A 2−form ω on X is said to be non-degenerate if, for each q ∈ X and for each nonzero vector v in the tangent space TqX, there is a tangent vector v ∈ TqX such that ω(u, v) 6= 0. A symplectic structure onX is a non-degenerate closed 2−form. The fundamental example of a symplectic structure is ω0 = ∑ i dxi ∧ dyi on R = {(x1, y1, ..., xn, yn)}. In fact, b...

A Hermitian metric on a complex manifold is called SKT (strong Kähler with torsion) if the Bismut torsion 3-form [Formula: see text] closed. As conformal generalization of condition, we introduce new type structure, locally (or shortly LCSKT). More precisely, structure said to be LCSKT there exists closed nonzero text]-form such that text]. In this paper, consider nontrivial structures, i.e. as...

Our main results are: (1) The complex and Lagrangian points of a non-complex and nonLagrangian 2n-dimensional submanifold F :M →N , immersed with parallel mean curvature and with equal Kähler angles into a Kähler-Einstein manifold (N, J, g) of complex dimension 2n, are zeros of finite order of sin θ and cos θ respectively, where θ is the common J-Kähler angle. (2) If M is a Cayley submanifold o...

This paper is a sequel of [8]. In algebraic geometry, when discussing the compactification of the moduli space of complex manifold X with ample canonical bundle KX , it is necessary to consider holomorphic degeneration family π : X → B, where Xt = π(t) are smooth for t 6= 0, X and X0 are QGorenstein, such that the canonical bundle of Xt for t 6= 0 and the dualizing sheaf of X0 are ample. We wil...

We construct a polarized Hodge structure on the primitive part of Chen and Ruan’s orbifold cohomology Hk orb(X) for projective SL-orbifolds X satisfying a “Hard Lefschetz Condition”. Furthermore, the total cohomology ⊕ p,q H p,q orb(X) forms a mixed Hodge structure that is polarized by every element of the Kähler cone of X. Using results of Cattani-Kaplan-Schmid this implies the existence of an...

We confirm the leading α′3 correction to the 4d, N = 1 Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the α′3-modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected...

In this paper we present a two-field inflation model, which distinguishes itself with a non-canonical kinetic lagrangian and comes from the large volume approach to the moduli stabilization in flux compactification of type IIB superstring on a Calabi-Yau orientifold of h(1,2) > h(1,1) ≥ 4. The Kähler moduli are classified as volume modulus, heavy moduli and two light moduli. The axion-dilaton, ...