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Kähler Normal Coordinates on Kählerian Symmetric Spaces
Jueves 13 Agosto 2015, 05:00pm
Accesos : 156

Fecha: 13 de Agosto, 2015. 5pm.

 

Expositor: Tillmann Jentsch

 

Actividad: Coloquio Oaxaqueño del Instituto de Matemáticas de la UNAM.

 

Lugar: Instituto de Matemáticas Unidad Oaxaca

 

Resumen:

 

 On every Kähler manifold and for any point in the Kähler manifold there exists a distinguished coordinate system around the point called Kählerian normal coordinates. It is characterized by the property that the complexified Taylor expansion of the components of the Hermitian tensor do not contain purely holomorphic or anti-holomorphic terms except for the constant term. An equivalent formulation can be given via the Kähler potential which is uniquely determined in Kählerian normal coordinates. Although this definition is well known since the work of E. Kähler, explicit examples are seemingly  unknown. Together with Dr. Gregor Weingart, I found explicit examples for certain Kählerian symmetric spaces, namely for the complex Grassmannians and the complex quadrics. In particular, we found that these formulas for Kählerian normal coordinates are surprinsingly easy to understand.

 

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