Related papers: Austere Submanifolds in Complex Projective Space

We discuss the problem of classifying birational extremal contractions of smooth threefolds where the canonical bundle is trivial along the curves contracted, in the case when a divisor is contracted to a point. We prove the analytic…

We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$…

As part of a programme to classify quasi-Einstein metrics $(M,g,X)$ on closed manifolds and near-horizon geometries of extreme black holes, we study such spaces when the vector field $X$ is divergence-free but not identically zero. This…

For an element $\Psi$ in the graded vector space $\Omega^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, a $\Psi$-submanifold is defined as a submanifold $N$ of $M$ such that $\Psi_{|N} \in \Omega^*(N, TN)$. The class of…

The notion of poor manifolds was introduced by Bandman and Zarhin, who asked for their classification. We study poor compact K\"ahler manifolds, i.e. those containing no rational curves and no codimension-one analytic subvarieties. We…

We find a new class of invariant metrics existing on the tangent bundle of any given almost-Hermitian manifold. We focus here on the case of Riemannian surfaces, which yield new examples of K\"ahlerian Ricci-flat manifolds in four real…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

Let $C\to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton-Cartan equations for a gauge-invariant Lagrangian density $\Lambda $ on $C$ satisfying a weak condition of regularity, are shown to admit an…

Let $S$ be a minimal surface of general type with irregularity $q(S) = 1$. Well-known inequalities between characteristic numbers imply that $3 p_g(S) \le c_2(S) \le 10 p_g(S)$, where $p_g(S)$ is the geometric genus and $c_2(S)$ the…

Complex supermanifold structures being deformations of the exterior algebra of a holomorphic vector bundle, have been parametrized by orbits of a group on non-abelian cohomology by P. Green. For the case of odd dimension $4$ and $5$ an…

We provide new examples of manifolds which admit a Riemannian metric with sectional curvature nonnegative, and strictly positive at one point. Our examples include the unit tangent bundles of $CP^n$, $HP^n$ and $CaP^2$, and a family of lens…

Let $M$ be a compact hyperkahler manifold equipped with a Lagrangian fibration $\pi:\; M \to X$, and $M'$ the smooth locus of $\pi$. We prove that over a complement to a codimension $\geq 2$ subset in $X$, the projection $\pi:\; M' \to X$…

Given a compact smooth totally real immersed $n$-submanifold $M\subset\mathbb C^n$ with only finitely many transverse double points, it is known that if $M$ is Lagrangian with respect to some K{\"a}hler form on $\mathbb C^n$, then it is…

We study special Lagrangian submanifolds in the Calabi-Yau manifold $T^*S^n$ with the Stenzel metric, as well as calibrated submanifolds in the $\text{G}_2$-manifold $\Lambda^2_-(T^*X)$ $(X^4 = S^4, \mathbb{CP}^2)$ and the…

We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case there exists a one-to-one correspondence between algebras of…

Riemannian four-manifolds in which the triple contraction of the curvature tensor against itself yields a functional multiple of the metric are called weakly Einstein. We focus on weakly Einstein K\"ahler surfaces. We provide several…

We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

We study several classes of Riemannian manifolds which are defined by imposing a certain condition on the Ricci tensor. We consider the following cases: Ricci recurrent, Cotton, quasi Einstein and pseudo Ricci symmetric condition. Such…

Considering pseudo-Riemannian $g$-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure…