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    Query regarding classification of pde

    In my research work, I recently have come across a system of three linear first order pde's whose characteristic polynomial has one real and two complex conjugate zeros. I have searched the available resources and could nowhere find out which category (elliptic/hyperbolic/parabolic) it falls...
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    How does Lie group help to solve ode's?

    Being not an expert, my question might sound naive to students of mahematics. My question is how on earth a Lie group helps to solve an ode. Can anyone explain me in simple terms?
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    Why there cannot be a single chart for n-sphere?

    My question is about a general comment made in differential geometry books: There cannot be a single chart for the manifold n-sphere. I have been trying a proof for long but ... Can you help me out?
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    Differential manifold without connection: Is it possible?

    We all are familiar with the kind of differential geometry where some affine connection always exists to relate various tangent spaces distributed over the manifold, and from this connection two fundamental tensors, namely the Cartan's torsion and the Riemann-Christoffel curvature, arise. Is it...
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    Topological classification of defects

    Please help somebody on this problem... When we topologically classify the defects in ordered media, we consider the character of the fundamental group of the associated order parameter space. To construct those groups, we circumscribe the line defects by circles and the point defects by...