Related papers: Universal curvature identities and Euler Lagrange …

We obtain a generalization, for a general compact almost complex manifold, of the well-known K\"{a}hler (or Hodge) identities for K\"{a}hler manifolds involving the commutators of the exterior differential and the Lefschetz operator and its…

Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…

The goal of this paper is to present Euler-Lagrange and Hamiltonian equations on R2n which is a model of para-Kaehlerian manifolds of constant J-sectional curvature. In conclusion, some differential geometrical and physical results on the…

We fully classify all Lagrangian submanifolds of a complex Grassmannian which are an orbit of a compact group of isometries and have positive Euler characteristic.

We introduce the $\Gamma$-Euler-Satake characteristics of a general orbifold $Q$ presented by an orbifold groupoid $\mathcal{G}$, generalizing to orbifolds that are not necessarily global quotients the generalized orbifold Euler…

The properties of Kaehler submanifolds with recurrent the second fundamental form in spaces of constant holomorphic sectional curvature are being studied in this article.

This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…

A novel approach for Lagrange formulation for field theories is proposed in terms of Kawaguchi geometry (areal metric space). On the extended configuration space M for classical field theory composed of spacetime and field configuration…

The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous…

We show that a compact quaternionic-K\"ahler manifold with positive scalar curvature and nonnegative sectional curvature is isometric to a symmetric space. This extends a classical theorem of Berger.

Equivalence classes of $n$-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger…

An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give various characterizations of scalar curvature rigidity for…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

We study integrable Euler equations on the Lie algebra $\mathfrak{gl}(3,\mathbb{R})$ by interpreting them as evolutions on the space of hexagons inscribed in a real cubic curve.

We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either…

We determine all the equivariant Euler characteristics of the building for the general unitary group over a finite field.

This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics…

Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp. 499-505, Podvigina et al., J. Comput. Phys.,…

We establish inequalities for the eigenvalues of Schr\"{o}dinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related…

In this paper, we establish new Laplacian comparison theorems and rigidity theorems for complete K\"ahler manifolds under new curvature notions that interpolate between Ricci curvature and holomorphic bisectional curvature.