Holomorphic submersions from Stein manifolds

Holomorphic Submersions from Stein Manifolds

Holomorphic Submersions from Stein Manifolds

Isometric Submersions of Finsler Manifolds

The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.

Holomorphic fiber bundle with Stein base and Stein fibers

A surjective holomorphic map Π : X → Y between complex spaces is said to be a Stein morphism, if for every point y ∈ Y , there exists an open neighborhood U of y such that Π(U) is Stein. In 1977, Skoda [12] showed that a locally trivial analytic fiber bundle Π : X → Ω with Stein base and Stein fibers is not necessarily a Stein manifold. Thus giving a negative answer to a conjecture proposed in ...

Plateau–Stein Manifolds

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f . We show, for instance, that if an X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurfac...