Descrip.
RESUMEN
H. Hopf
has introduced the use of holomorphic quadratic forms
to study surfaces with constant mean curvature in R3. The same techniques have been used to study surfaces
immersed in spaces forms, complex projective spaces also to study harmonic mape. Following Hopf’s ideas we
consider holomorphic type forms, that is, forms whose
zeroes behave like zeroes of holomorphic forms, to
study surfaces such that the norm of the mean curvature vector or of its
covariant derivate satisfies some inequality. We also apply the same techniques
to study maps whose tension field satisfies similar property.
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