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1988•Pacific Journal of MathematicsOpen access

Abstract Riemannian stratifications

G. Monti Bragadin

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Abstract

Let A be an abstract stratification.Assume that every stratum X is a riemannian manifold.We first give some conditions, under which it is possible to endow A with a suitable metric extending a well known technique of riemannian manifolds.Then stronger conditions are introduced in order that the metric space A becomes a G-space.An abstract stratification with all the above conditions is called an abstract riemannian stratification.Whitney stratifications are, in a natural way, riemannian.

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Let A be an abstract stratification.Assume that every stratum X is a riemannian manifold.We first give some conditions, under which it is possible to endow A with a suitable metric extending a well known technique of riemannian manifolds.Then stronger conditions are introduced in order that the metric space A becomes a G-space.An abstract stratification with all the above conditions is called an abstract riemannian stratification.Whitney stratifications are, in a natural way, riemannian.

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Available abstract

Let A be an abstract stratification.Assume that every stratum X is a riemannian manifold.We first give some conditions, under which it is possible to endow A with a suitable metric extending a well known technique of riemannian manifolds.Then stronger conditions are introduced in order that the metric space A becomes a G-space.An abstract stratification with all the above conditions is called an abstract riemannian stratification.Whitney stratifications are, in a natural way, riemannian.

Key concepts: Mathematics, Stratification (seeds), Riemannian geometry, Pure mathematics, Riemannian manifold, Manifold (fluid mechanics), Fundamental theorem of Riemannian geometry, Mathematical analysis

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