Related papers: Morse-type integrals on non-K\"ahler manifolds

In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities.…

We discuss pluripotential aspects of the Monge-Amp\`ere equations on compact Hermitian manifolds and prove $L^{\infty}$ estimates for any metric, as well as the existence of weak solutions under an extra assumption.

In this paper we establish partial structure results on the geometry of compact Hermitian manifolds of semipositive Griffiths curvature. We show that after appropriate arbitrary small deformation of the initial metric, the null spaces of…

This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain compacti- fied moduli spaces, orientation formulas, and CW…

We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to…

Mabuchi introduced multiplier Hermitian structures on compact Kahler manifolds and defined metrics similar to Kahler-Einstein metrics under these structures. In this note we generalize the inequality of Moser-Trudinger type on…

In this paper, we derive an \emph{a priori} second order estimate for solutions which are in $\Gamma_{k+1}$ cone to a class of complex Hessian equations with both sides of the equation depending on the gradient on compact Hermitian…

Theorems of Barth-Lefschetz type describe restrictions on the topology of varieties of small codimension. R. Schoen and J. Wolfson, using Morse theory on a path space, have described a technique to prove theorems of this kind for complex…

In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…

Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-K\"ahler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized…

In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric…

Let F be a Riemannian submersion from an almost Hermitian manifold (M; gM; J) onto a Riemannian manifold (N; gN). We introduce the notion of the v-semi-slant submersion. And then we obtain some properties on it. In particular, we give some…

We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…

We show that a quasi-geodesic in an injective metric space is Morse if and only if it is strongly contracting. Since mapping class groups and, more generally, hierarchically hyperbolic groups act properly and coboundedly on injective metric…

We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.

We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our…

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be K\"ahler. The main result of this…

Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-K\"ahler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-K\"ahler…

We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous manifolds and discuss when this metric is complete and K\"ahler. This construction has a strong interplay…

A Sim(n-1,1) affine manifold is an affine manifold whose linear holonomy is contained in the similarity lorentzian group but not in the lorentzian group. The class of similarity lorentzian affine manifolds is a small part in the nice class…