Presentation Title

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.

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Nov 8th, 3:00 PM Nov 8th, 5:00 PM

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.