Cauchy-Riemann vector fields

On symmetric Cauchy-Riemann manifolds

The Riemannian symmetric spaces play an important role in different branches of mathematics. By definition, a (connected) Riemannian manifold M is called symmetric if, to every a ∈ M , there exists an involutory isometric diffeomorphism sa:M → M having a as isolated fixed point in M (or equivalently, if the differential dasa is the negative identity on the the tangent space Ta = TaM of M at a)....

On Three-dimensional Cauchy-riemann Manifolds

of the almost complex tensor of C2 ("multiplication by i "). The collection of these subspaces HpM forms a bundle H MeT M called the horizontal or contact bundle. (Indeed, strict pseudoconvexity of M implies that the plane field {HpM} is nondegenerate, i.e. defines a contact structure.) The almost complex tensor of C2 then restricts to a bundle endomorphism J : H M -+ H M such that J2 = -id. Th...

Principal Toroidal Bundles over Cauchy - Riemann Products

The main result we obtain is that given t N M a TS-subbundle of the generalized Hopf fibration t H2+’cP over a Cauchy-Riemann product M _ cP, i.e. N _ H is a diffeomorphism on fibres and oj= ot, if s is even and N is a closed submanifold tangent to the structure vectors of the canonical 5Zstructure on H then N is a Cauchy-Riemann submanifold whose Chen class is non-vanishing.

Cauchy-stieltjes and Riemann-stielt Jes Integrals

The Cauchy-riemann Equations and Differential Geometry