A Willmore functional for compact surfaces of complex projective plane

Details A Willmore functional for compact surfaces of complex projective plane A Willmore functional for compact surfaces of complex projective plane

2000-02-18

arxiv.org/abs/math/0002155v1

Mathematics

Differential Geometry

30 pages

Scientific paper

We propose the study of a conformally invariant functional for surfaces of complex projective plane which is closely related to the classical Willmore functional. We show that minimal surfaces of complex projective plane are critical for this functional and construct some minima for it via the twistors spaces of complex projective plane. Also, we find lower bounds for this functional and for its restriction to the class of Lagrangian surfaces and characterize the complex lines and the Lagrangian totally geodesic surfaces and the Whitney spheres as the only attaining those bounds.

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