منابع مشابه
Existence of Engel structures
We develop a construction of Engel structures on 4– manifolds based on decompositions of manifolds into round handles. This allows us to show that all parallelizable 4–manifolds admit an Engel structure. We also show that, given two Engel manifolds M1, M2 satisfying a certain condition on the characteristic foliations, there is an Engel structure on M1#M2#(S ×S) which is closely related to the ...
متن کاملHolomorphic Engel Structures
Recently there has been renewed interest among differential geometers in the theory of Engel structures. We introduce holomorphic analogues of these structures, and pose the problem of classifying projective manifolds admitting them. Besides providing the basic properties of these varieties, we present two series of examples and characterize them by certain positivity conditions on the Engel st...
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A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined locally by 3 vector fields that play the role of an orthonormal frame, but could become collinear on some set Z called the singular set. Under the Hormander condition, a 3D almost-Riemannian structure still has a metric space structure, whose topology is compatible with the original topology of the manifold. Almost-Rie...
متن کاملEngel structures with trivial characteristic foliations
Engel structures on M×S and M×I are studied in this paper, where M is a 3–dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S or I . It is proved that they are characterized by contact structures on the cross section M , the twisting numbers, and Legendrian foliations on both ends M × ∂I in the case of M × I . AMS Classification 57R25...
متن کاملOn Hessian Riemannian Structures
In Proposition 4.1 a characterization is given of Hessian Rieman-nian structures in terms of a natural connection in the general linear group GL(n; R) + , which is viewed as a principal SO(n)-bundle over the space of positive deenite symmetric n n-matrices. For n = 2, Proposition 5.3 contains an interpretation of the curvature of a Hessian Riemannian structure at a given point, in terms of an u...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2020
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnaa211