Real and Complex Submanifolds pp 319-327 | Cite as

# The Fixed Point Set of a Holomorphic Isometry and the Intersection of Two Real Forms in the Complex Grassmann Manifold

## Abstract

We study the fixed point set of a holomorphic isometry of the complex Grassmann manifold and the intersection of two real forms which are congruent to the real Grassmann manifold. Furthermore, we investigate the relation between them.

## Keywords

Real Form Identity Component Grassmann Manifold Hermitian Symmetric Space Riemannian Symmetric Space## Notes

### Acknowledgements

The first author was partly supported by the Grant-in-Aid for Science Research (C) 2013 (No. 25400070), Japan Society for the Promotion of Science. The second author was partly supported by the Grant-in-Aid for Science Research (C) 2013 (No. 23540108), Japan Society for the Promotion of Science. The third author was partly supported by the Grant-in-Aid for Science Research (C) 2013 (No. 24540064), Japan Society for the Promotion of Science.

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