The Continuity Equation, Hermitian Metrics and Elliptic Bundles

We extend the continuity equation of La Nave–Tian to Hermitian metrics and establish its interval of maximal existence. The equation is closely related to the Chern–Ricci flow, and we illustrate this in the case of elliptic bundles over a curve of genus at least two.

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Veröffentlicht in:	The Journal of Geometric Analysis 2020, Vol.30 (1), p.762-776
Hauptverfasser:	Sherman, Morgan, Weinkove, Ben
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Bundles Continuity equation Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
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Beschreibung
Zusammenfassung:	We extend the continuity equation of La Nave–Tian to Hermitian metrics and establish its interval of maximal existence. The equation is closely related to the Chern–Ricci flow, and we illustrate this in the case of elliptic bundles over a curve of genus at least two.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-019-00168-5