Related papers: Generalized CRF-structures

In an earlier paper, we studied manifolds $M$ endowed with a generalized F structure $\Phi\in End(TM\oplus T^*M)$, skew-symmetric with respect to the pairing metric, such that $\Phi^3+\Phi=0$. Furthermore, if $\Phi$ is integrable (in some…

We establish the conditions for the induced generalized metric F structure of an oriented hypersurface of a generalized K\"ahler manifold to be a generalized CRFK structure. Then, we discuss a notion of generalized almost contact structure…

Let $M$ be a smooth manifold, let $TM$ be its tangent bundle and $T^{*}M$ its cotangent bundle. This paper investigates integrability conditions for generalized metrics, generalized almost para-complex structures, and generalized Hermitian…

We define a generalized almost para-Hermitian structure to be a commuting pair $(\mathcal{F},\mathcal{J})$ of a generalized almost para-complex structure and a generalized almost complex structure with an adequate non-degeneracy condition.…

We introduce a generalization of structured manifolds as the most general Riemannian metric g associated to an affinor (tensor field of (1,1)-type) F and initiate a study of their semi-invariant submanifolds. These submanifolds are…

An $f$-structure, introduced by K. Yano in 1963 and subsequently studied by a number of geometers, is a higher dimensional analog of almost complex and almost contact structures, defined by a (1,1)-tensor field $f$ on a $(2n+p)$-dimensional…

In this note, we consider submanifolds of a generalized K\"ahler manifold that are CR-submanifolds for the two associated Hermitian structures. Then, we establish the conditions for the induced, generalized F structure to be a CRFK…

Let E be a transitive Courant algebroid with scalar product of neutral signature. A generalized almost complex structure \mathcal J on E is a skew-symmetric smooth field of endomorphisms of E which squares to minus the identity. We say that…

In this paper we define the notion of a generalized coK\"ahler structure and prove that the product $M_{1}\times M_{2}$ of generalized contact metric manifolds $(M_i, \Phi_i,E_{\pm,i}, G_i)$, $ i=1, 2$, where $M_{1}\times M_{2}$ is endowed…

An $f$-structure on a manifold $M$ is an endomorphism field $\phi\in\Gamma(M,\End(TM))$ such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure $E_{1,0}\subset T_\C M$ given by the $+i$-eigenbundle of $\phi$.…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

On the generalized tangent bundle of a smooth manifold, we study skew-symmetric endomorphism satisfying an arbitrary polynomial equation with real constant coefficients. We study the compatibility of these structures with the de Rham…

For a Riemannian foliation $F$ on a compact manifold $M$ with a bundle-like metric, the de Rham complex of $M$ is $C^{\infty}$-splitted as the direct sum of the basic complex and its orthogonal complement. Then the basic component…

In the paper, we first study more general models, where $F$ has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric $f$-contact…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

We construct a generalization of Courant algebroids which are classified by the third cohomology group $H^3(A,V)$, where $A$ is a Lie Algebroid, and $V$ is an $A$-module. We see that both Courant algebroids and $\mathcal{E}^1(M)$ structures…

We consider Courant and Courant-Jacobi brackets on the stable tangent bundle $TM\times\mathds{R}^h$ of a differentiable manifold and corresponding Dirac, Dirac-Jacobi and generalized complex structures. We prove that Dirac and Dirac-Jacobi…

For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be…

We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B-field transform, by almost product and local product structures. We also introduce a pure spinor formalism for…

In this paper, we study the geometries given by commuting pairs of generalized endomorphisms ${\cal A} \in \text{End}(T\oplus T^*)$ with the property that their product defines a generalized metric. There are four types of such commuting…