How Do You Spell LEGENDRIAN?

1. Legendrian is an adjective that is primarily used in mathematics, specifically in the field of differential geometry and the study of smooth manifolds. It refers to a certain type of submanifold in a contact manifold. A contact manifold is a type of manifold equipped with a certain differential one-form, called a contact form, which imposes certain restrictions on the geometry of the manifold.

   A submanifold is said to be Legendrian if its tangent spaces are in a specific relation with the contact distribution of the manifold. In simpler terms, the submanifold is said to be "maximally tangent" to the contact planes. Legendrian submanifolds possess unique geometric properties and are of interest in the study of knot theory and symplectic geometry.

   The concept of Legendrian submanifolds finds significance in the context of symplectic topology, a branch of mathematics that explores the relationship between symplectic manifolds, which are smooth manifolds with a certain closed non-degenerate two-form, and their submanifolds. The study of Legendrian submanifolds involves analysis of their singularities, their intersection with other submanifolds, and their behavior under certain geometric transformations.

   In summary, the term "Legendrian" pertains to a specific type of submanifold in a contact manifold, and has applications in various branches of mathematics, including symplectic geometry and knot theory.

Common Misspellings for LEGENDRIAN

The word "Legendrian" is derived from the mathematical term "Legendre" and the suffix "-ian".

The term "Legendre" refers to Adrien-Marie Legendre, an influential French mathematician who lived in the 18th and 19th centuries. He made significant contributions to various fields of mathematics, including number theory, algebra, and calculus. Legendre's work on the theory of elliptic functions and differential equations is particularly notable.

The suffix "-ian" is a common suffix in English that is used to denote belonging or association. For instance, "Victorian" refers to the era of Queen Victoria, "Shakespearean" refers to works of William Shakespeare, and "Freudian" refers to the theories of Sigmund Freud.