Compact Hermitian Symmetric Spaces, Coadjoint Orbits, and the Dynamical Stability of the Ricci Flow

Using a stability criterion due to Kröncke, we show, providing n ≠ 2 k , the Kähler–Einstein metric on the Grassmannian G r k ( C n ) of complex k -planes in an n -dimensional complex vector space is dynamically unstable as a fixed point of the Ricci flow. This generalises the recent results of Krön...

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Vydáno v:	The Journal of geometric analysis Ročník 31; číslo 6; s. 6195 - 6218
Hlavní autoři:	Hall, Stuart James, Murphy, Thomas, Waldron, James
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.06.2021 Springer Nature B.V
Témata:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamic stability Dynamical Systems and Ergodic Theory Flow stability Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Orbits Stability criteria Ricci flow Symmetric space Stability of Einstein metrics
ISSN:	1050-6926, 1559-002X
On-line přístup:	Získat plný text
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Popis
Shrnutí:	Using a stability criterion due to Kröncke, we show, providing n ≠ 2 k , the Kähler–Einstein metric on the Grassmannian G r k ( C n ) of complex k -planes in an n -dimensional complex vector space is dynamically unstable as a fixed point of the Ricci flow. This generalises the recent results of Kröncke and Knopf–Sesum on the instability of the Fubini–Study metric on CP n for n > 1 . The key to the proof is using the description of Grassmannians as certain coadjoint orbits of SU ( n ). We are also able to prove that Kröncke’s method will not work on any of the other compact, irreducible, Hermitian symmetric spaces.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-020-00524-w