In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which...

the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is...

_{p})\,.} The third fundamental form is expressible entirely in terms of the first fundamental form and second fundamental form. If we let H be the mean...

form. The curvature and arc length of curves on the surface, surface area, differential geometric invariants such as the first and second fundamental...

operations can be thought of as inverses of each other. The first part of the theorem, the first fundamental theorem of calculus, states that for a continuous function...

can be calculated from the first fundamental form (also called metric tensor) of the surface. The second fundamental form, by contrast, is an object which...

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

normal form (dynamical systems). In the study of manifolds in three dimensions, one has the first fundamental form, the second fundamental form and the...

full knowledge of the first fundamental form and expressed via the first fundamental form and its partial derivatives of first and second order. Equivalently...

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental...

Sonata form (also sonata-allegro form or first movement form) is a musical structure generally consisting of three main sections: an exposition, a development...

quantity ds in (1) is called the line element, while ds2 is called the first fundamental form of M. Intuitively, it represents the principal part of the square...

integrating a Riemannian volume form on the parameterized surface, where the metric tensor is given by the first fundamental form of the surface. Consider a...

sets which can be smoothly embedded into R3 with first fundamental form g and second fundamental form (relative to one of the two choices of unit normal...

In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every...

holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological...

The Fundamental Rights in India enshrined in part III (Article 12–35) of the Constitution of India guarantee civil liberties such that all Indians can...

ensure that every fundamental discriminant corresponds uniquely to a specific type of quadratic form. The first eleven positive fundamental discriminants...

combination of the prior four forces in the form of a scalar field; such as the Higgs field. Each of the known fundamental interactions can be described mathematically...

(Lie theory), Exponential map (Riemannian geometry) Finsler metric First fundamental form for an embedding or immersion is the pullback of the metric tensor...

included 28 cinquains. Crapsey's American Cinquain form developed in two stages. The first, fundamental form is a stanza of five lines of accentual verse,...

distance on the sphere, d s {\displaystyle ds} is defined by the first fundamental form: d s 2 = [ d λ d ϕ ] [ E F F G ] [ d λ d ϕ ] {\displaystyle...

Gauss–Peterson–Codazzi formulas) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion...

Spurs in the National Basketball Association (NBA). Nicknamed "the Big Fundamental", he is widely regarded as the greatest power forward of all time and...

abstract form. A basic elaboration of the tonic triad, it consists of the fundamental line accompanied by the bass arpeggiation. Hence the fundamental structure...

In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model...

Fenchel's theorem Theorema egregium Gauss–Bonnet theorem First fundamental form Second fundamental form Gauss–Codazzi–Mainardi equations Dupin indicatrix Asymptotic...

The Fundamental Rights, Directive Principles of State Policy and Fundamental Duties are sections of the Constitution of India that prescribe the fundamental...

In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital...

first fundamental form g i j {\displaystyle g_{ij}} of the surface mapping f {\displaystyle f} is the identity matrix and the second fundamental form...