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A complex manifold for which the exterior derivative of the fundamental form Omega associated with the given Hermitian metric vanishes, so dOmega=0. In other words, it is a ...

A Kähler metric is a Riemannian metric g on a complex manifold which gives M a Kähler structure, i.e., it is a Kähler manifold with a Kähler form. However, the term "Kähler ...

The Kähler potential is a real-valued function f on a Kähler manifold for which the Kähler form omega can be written as omega=ipartialpartial^_f. Here, the operators ...

Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

Let f:A->B be a map between sets A and B. Let Y subset= B. Then the preimage of Y under f is denoted by f^(-1)(Y), and is the set of all elements of A that map to elements in ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...