Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds

Details Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds

2000-04-14

arxiv.org/abs/math/0004093v1

Mathematics

Differential Geometry

17 pages, plain LaTeX

Scientific paper

We define broadly-pluriminimal immersed 2n-submanifold F: M --> N into a Kaehler-Einstein manifold of complex dimension 2n and scalar curvature R. We prove that, if M is compact, n \geq 2, and R < 0, then: (i) Either F has complex or Lagrangian directions; (ii) If n = 2, M is oriented, and F has no complex directions, then it is a Lagrangian submanifold, generalising the well-known case n = 1 for minimal surfaces due to Wolfson. We also prove that, if F has constant Kaehler angles with no complex directions, and is not Lagrangian, then R = 0 must hold. Our main tool is a formula on the Laplacian of a symmetric function on the Kaehler angles.

Affiliated with

Also associated with

No associations

Rating

Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-544779