I'd like a hint for the following question: Show that in a elliptic point, principal directions bisects asymptotic directions. thanks.
Question about asymptotic direction
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differential-geometry
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1How do you define "elliptic points", "principal directions", and "asymptotic directions"? What book are you using to learn differential geometry? – 2011-11-06
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0I'm using Manfredo's book(Portuguese version) but there is a english version of it.Elliptic points are points whose Gaussian curvature is always positive, principal direction is a line generated by the eigenvectors of the self-adjoint transformation $DN_p$, asymptotic direction is a line generated by a vector which is tangent to a curve whose normal curvature is zero.I tried to use Euler's formula but get no result. – 2011-11-07