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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

1 vote
1 answer
712 views

Mean curvature calculated using second order derivation of the second fundamental form

Is there a formula for calculating the mean curvature tensor using Ricci tensor, Gauss curvature tensor and the second order derivative of the second fundamental form? More precisely, I found some for …
3 votes
2 answers
448 views

Jordan algebra and quaternionic projective space

How we can define quaternionic projective space and metric on it using Jordan algebra? Thank you in advance!
1 vote
3 answers
381 views

Totally complex submanfiolds in quaternionic Kaehlerian manifolds

Hello, I would like to know some examples of totally complex submanifolds in quaternionic Kaehlerian manifolds, is there any references in which I could find them? So far I could not find. Also, the …
0 votes
0 answers
308 views

Quaternion Kaehlerian manifold, definition

Hello, I am reading the paper of S. Ishihara, Quaternion Kaehlerian manifolds, I need it for understanding of totally complex submanifolds in quaternion Kaehlerian manifolds. I am afraid that I don't …