P-30 A note on an inequality of Riemannian submersion invariant
Presenter Status
Department of Mathematics
Location
Buller Hallway
Start Date
8-11-2012 3:00 PM
End Date
8-11-2012 5:00 PM
Presentation Abstract
It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with totally geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal submanifold. B.Y. Chen proved this using an inequality involving the submersion invariant and his inequality shows the maximum value of the invariant. I could find another inequality that gives the minimum of the submersion invariant under a certain assumption.
P-30 A note on an inequality of Riemannian submersion invariant
Buller Hallway
It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with totally geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal submanifold. B.Y. Chen proved this using an inequality involving the submersion invariant and his inequality shows the maximum value of the invariant. I could find another inequality that gives the minimum of the submersion invariant under a certain assumption.