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ON THE GEOMETRY OF SEMI{RIEMANNIAN DISTRIBUTIONS

Aurel Bejancu, Hani Reda Farran

Open publisher page 6 citations

Abstract

We prove the existence and uniqueness of a linear connection on a semi{ Riemannian distribution which satisfles similar conditions as the Levi{Civita connection on a semi{Riemannian manifold. When the ambient manifold is semi{Riemannian too, we study its geometrical properties related to two orthogonal complementary distributions. Finally, we construct a non{holonomic manifold on which a bundle{like metric exists. Mathematics Subject Classiflcation 2000: 53C07, 53C12.

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What this paper is about

We prove the existence and uniqueness of a linear connection on a semi{ Riemannian distribution which satisfles similar conditions as the Levi{Civita connection on a semi{Riemannian manifold. When the ambient manifold is semi{Riemannian too, we study its geometrical properties related to two orthogonal complementary distributions. Finally, we construct a non{holonomic manifold on which a bundle{like metric exists. Mathematics Subject Classiflcation 2000: 53C07, 53C12.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove the existence and uniqueness of a linear connection on a semi{ Riemannian distribution which satisfles similar conditions as the Levi{Civita connection on a semi{Riemannian manifold. When the ambient manifold is semi{Riemannian too, we study its geometrical properties related to two orthogonal complementary distributions. Finally, we construct a non{holonomic manifold on which a bundle{like metric exists. Mathematics Subject Classiflcation 2000: 53C07, 53C12.

Key concepts: Mathematics, Pseudo-Riemannian manifold, Connection (principal bundle), Statistical manifold, Fundamental theorem of Riemannian geometry, Levi-Civita connection, Riemannian geometry, Metric connection

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