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The class of second order ODE's cubic with respect to the first orderderivative is considered. Using geometric structures associated with theseequations, the subclasses of umbilical equations, zero mean curvatureequations, and zero Gaussian curvature equations are defined. Zero meancurvature equations are studied within the framework of the first case ofintermediate degeneration with the stress on their pseudoscalar and scalarinvariants.

Umbilical and zero curvature equations in a class of second order ODE's