Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Rigidity of pseudo-holomorphic curves of constant curvature in Grassmann manifolds


Authors: Quo-Shin Chi and Yunbo Zheng
Journal: Trans. Amer. Math. Soc. 313 (1989), 393-406
MSC: Primary 53C42; Secondary 53C55
MathSciNet review: 992602
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Rigidity of minimal immersions of constant curvature in harmonic sequences generated by holomorphic curves in Grassmann manifolds is studied in this paper by lifting them to holomorphic curves in certain projective spaces. We prove that for such curves the curvature must be positive, and that all such simply connected curves in $ C{P^n}$ are generated by Veronese curves, thus generalizing Calabi's counterpart for holomorphic curves in $ C{P^n}$. We also classify all holomorphic curves from the Riemann sphere into $ G(2,4)$ whose curvature is equal to $ 2$ into two families, which illustrates pseudo-holomorphic curves of positive constant curvature in $ G(m,N)$ are in general not unitarily equivalent, constracting to the fact that generic isometric complex submanifolds in a Kaehler manifold are congruent.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C42, 53C55

Retrieve articles in all journals with MSC: 53C42, 53C55


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0992602-9
PII: S 0002-9947(1989)0992602-9
Keywords: Pseudo-holomorphic curves, Grassmann manifolds, Veronese curves
Article copyright: © Copyright 1989 American Mathematical Society