KONDO THEORY FOR SPHERICAL SHELL TECTONICS

Abstract

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.