Kondo theory for spherical shell tectonics

The buckling phenomenon of a flat or spherical shell lithosphere (tectonic plate) has been investigated in previous research. However, these studies do not give information regarding the curvature effect in the buckling phenomenon. Kondo applied Riemannian geometry to the yielding or buckling of curved materials. When the Riemannian manifold (V_n dimensional manifold) with a nonzero Euler-Schouten curvature tensor is manifested in the enveloping manifold (Euclid space: V_m dimensional manifold), the included Riemannian manifold (dimension V_n) protrudes into the enveloping manifold (dimension V_m). The curvature effect for the buckling phenomenon of materials can be formulated by a force-balance equation from mechanics and the Euler-Schouten curvature tensor from differential geometry. In this paper, using the Euler-Schouten curvature tensor from differential geometry, the authors derive a formulation for the buckling phenomenon with the curvature effect for a spherical shell lithosphere as a buckling equation with high-order strain for lithosphere deformation.