Collapse of warped submersions

Spectra of Submersions

This talk presents a review of the results concerning the spectra of submersions obtained during the time by the author and others. Let (M, g), (B, j) be two connected compact Riemannian manifolds without boundary and let π : M −→ B be a submersion. We investigate the relations between the spectra of the LaplaceBeltrami operators acting on functions defined respectively on M , on B and on the f...

Bounded Riemannian Submersions

In this paper, we establish global metric properties of a Riemannian submersion π : Mn+k → Bn for which the fundamental tensors are bounded in norm: |A| ≤ CA, |T | ≤ CT . For example, if B is compact and simply connected, then there exists a constant C = C(B,CA, CT , k) such that for all p ∈ B, dFp ≤ C · dM , where dFp denotes the intrinsic distance function on the fiber Fp := π−1(p), and dM de...

Poincaré Submersions

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S1 yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.

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 Submersions from Stein Manifolds