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We study the 2-jet bundle of mappings of the real plane into a manifold. We shall prove that there exists an imbedding of this 2-jet bundle into a suitable first order jet bundle, in such a way that its image is the set of fixed points of a canonical automorphism of the biggest jet bundle.
We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...
Let be a real submanifold of an almost complex manifold and let be the maximal holomorphic subspace, for each . We prove that , is upper-semicontinuous.
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