ﻻ يوجد ملخص باللغة العربية
We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that of Poisson-Nijenhuis structures. We study several properties of the Dirac-Nijenhuis structures thus obtained, including their connection with holomorphic Dirac structures, the geometry of their leaves and quotients, as well as the presence of hierarchies. We also consider their integration to Lie groupoids, which includes the integration of holomorphic Dirac structures as a special case.
Adopting the omni-Lie algebroid approach to Dirac-Jacobi structures, we propose and investigate a notion of weak dual pairs in Dirac-Jacobi geometry. Their main motivating examples arise from the theory of multiplicative precontact structures on Lie
Let $S$ be a compact oriented finite dimensional manifold and $M$ a finite dimensional Riemannian manifold, let ${rm Imm}_f(S,M)$ the space of all free immersions $varphi:S to M$ and let $B^+_{i,f}(S,M)$ the quotient space ${rm Imm}_f(S,M)/{rm Diff}^
We give the strong form and weak form of the square of Nijenhuis tensor, study their properties, and give some applications.
The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie sub
We show how to assign to any immersed torus in $R^3$ or $S^3$ a Riemann surface such that the immersion is described by functions defined on this surface. We call this surface the spectrum or the spectral curve of the torus. The spectrum contains imp