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searching for Induced metric 34 found (47 total)

Metric space (11,073 words) [view diff] exact match in snippet view article find links to article

space by measuring distances the same way we would in M. Formally, the induced metric on A is a function d A : A × A → R {\displaystyle d_{A}:A\times A\to

Metric tensor (8,861 words) [view diff] exact match in snippet view article find links to article

for m = 3, which means that the ambient Euclidean space is ℝ3, the induced metric tensor is called the first fundamental form. Suppose that φ is an immersion

Polar action (164 words) [view diff] exact match in snippet view article find links to article

geodesic. If the sections of a polar action are flat with respect to the induced metric, then the action is called hyperpolar. In the case of linear orthogonal

Normed vector space (2,901 words) [view diff] exact match in snippet view article find links to article

V {\displaystyle V} . A norm induces a distance, called its (norm) induced metric, by the formula d ( x , y ) = ‖ y − x ‖ . {\displaystyle d(x,y)=\|y-x\|

Kadison–Kastler metric (234 words) [view diff] exact match in snippet view article find links to article

distance between the unit balls of the two C*-algebras, under the norm-induced metric on the space of all bounded operators on that Hilbert space. It was

Gauss–Codazzi equations (2,482 words) [view diff] exact match in snippet view article find links to article

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

Laplace operators in differential geometry (1,099 words) [view diff] exact match in snippet view article find links to article

spectrum Hodge differential forms metric induced metric and connection positive Connection tensors metric induced metric and connection negative Bochner any

De Sitter space (2,198 words) [view diff] exact match in snippet view article find links to article

space is the metric induced from the ambient Minkowski metric. The induced metric is nondegenerate and has Lorentzian signature. (Note that if one replaces

Bosonic string theory (1,601 words) [view diff] exact match in snippet view article find links to article

Polyakov formulation, g {\displaystyle g} is not to be understood as the induced metric from the embedding, but as an independent dynamical field. G {\displaystyle

Geodesic manifold (411 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {R} ^{2}\smallsetminus \lbrace 0\rbrace } (with its induced metric). Geodesics going to the origin cannot be defined on the entire real

Kähler manifold (4,476 words) [view diff] exact match in snippet view article find links to article

curvature.) For example, every complex submanifold of Cn (with the induced metric from Cn) has holomorphic sectional curvature ≤ 0. For holomorphic maps

Second fundamental form (1,454 words) [view diff] exact match in snippet view article find links to article

a Riemannian manifold (M,g) then the curvature tensor RN of N with induced metric can be expressed using the second fundamental form and RM, the curvature

Newtonian dynamics (1,334 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \displaystyle M} . The components of the metric tensor of this induced metric are given by the formula where ( , ) {\displaystyle \displaystyle

Beltrami equation (10,901 words) [view diff] exact match in snippet view article find links to article

f_{z}}\,d{\overline {z}}\right|^{2}.} The Beltrami quotient of this induced metric is defined to be f z ¯ / f z {\displaystyle f_{\overline {z}}/f_{z}}

Hilbert metric (1,144 words) [view diff] exact match in snippet view article find links to article

multiplicative constant. If the cone K is the positive orthant in Rn then the induced metric on the projectivization of K is often called simply Hilbert's projective

Banach space (17,214 words) [view diff] exact match in snippet view article find links to article

translation invariant distance function, called the canonical or (norm) induced metric, defined for all vectors x , y ∈ X {\displaystyle x,y\in X} by d ( x

Equivalence of metrics (1,023 words) [view diff] exact match in snippet view article find links to article

\mathbb {N} }} is Cauchy but not convergent. (It is not Cauchy in the induced metric.) Bishop and Goldberg, p. 10. Ok, p. 137, footnote 12. Carothers 2000

Glossary of Riemannian and metric geometry (2,072 words) [view diff] exact match in snippet view article find links to article

space a simplicial complex with a metric such that each simplex with induced metric is isometric to a simplex in Euclidean space. Principal curvature is

Irrational number (5,253 words) [view diff] exact match in snippet view article find links to article

metric space. Since the subspace of irrationals is not closed, the induced metric is not complete. Being a G-delta set—i.e., a countable intersection

Unit tangent bundle (881 words) [view diff] exact match in snippet view article find links to article

g_{H}(v,w)=g(v,w),\quad v,w\in H} and defining the metric on V as the induced metric from the embedding of the fiber UTxM into the Euclidean space TxM. Equipped

Spherically symmetric spacetime (1,784 words) [view diff] exact match in snippet view article find links to article

spacetime metric induces a metric on each orbit 2-sphere (and this induced metric must be a multiple of the metric of a 2-sphere). Conventionally, the

Umbilical point (1,499 words) [view diff] exact match in snippet view article find links to article

(vector-valued) Second fundamental form is some normal vector tensor the induced metric (First fundamental form). Equivalently, for all vectors U, V at p, II(U

Gershgorin circle theorem (2,479 words) [view diff] exact match in snippet view article find links to article

i.e., the quotient space of C^n under permutation equivalence with induced metric). Whichever continuity is used in a proof of the Gerschgorin disk theorem

Schur's lemma (Riemannian geometry) (2,522 words) [view diff] exact match in snippet view article

{\displaystyle h} is the second fundamental form, g {\displaystyle g} is the induced metric, and H {\displaystyle H} is the mean curvature tr g ⁡ h . {\displaystyle

Σ-algebra (5,337 words) [view diff] exact match in snippet view article find links to article

equivalence class, the resulting quotient set can be properly metrized by the induced metric. If the measure space is separable, it can be shown that the corresponding

Dirac membrane (1,542 words) [view diff] exact match in snippet view article find links to article

}=-{\frac {\omega }{4\pi }}\int _{x^{1}=0}Mdx^{0}dx^{2}dx^{3}} where the induced metric and the factors J and M are given by g μ ν = ∂ μ y Λ ∂ ν y Λ ,

Schwarzschild coordinates (4,089 words) [view diff] exact match in snippet view article find links to article

\sin \phi ),\;\;\partial _{\phi }=(0,-r\sin \phi ,r\cos \phi )} The induced metric inherited when we restrict the Euclidean metric on E3 to our parameterized

Lifting property (2,651 words) [view diff] exact match in snippet view article find links to article

the obvious inclusion between the two subspaces of the real line with induced metric, and { 0 } {\displaystyle \{0\}} is the metric space consisting of a

Fubini–Study metric (5,292 words) [view diff] exact match in snippet view article find links to article

manifold (X,g), then in order for the orbit space X/G to possess an induced metric, g {\displaystyle g} must be constant along G-orbits in the sense that

Limit of a function (11,103 words) [view diff] exact match in snippet view article find links to article

Dm(f ) of R {\displaystyle \mathbb {R} } as a metric space with the induced metric. In non-standard calculus the limit of a function is defined by: lim

Positive energy theorem (3,567 words) [view diff] exact match in snippet view article find links to article

together with a continuous unit normal vector field, such that the induced metric is g and the second fundamental form with respect to the given unit

Optical scalars (2,874 words) [view diff] exact match in snippet view article find links to article

{\displaystyle h^{ab}=g^{ab}+l^{a}n^{b}+n^{a}l^{b}} represents the induced metric. Also, θ ( ℓ ) {\displaystyle \theta _{(\ell )}} and θ ( n ) {\displaystyle

Complete topological vector space (15,843 words) [view diff] exact match in snippet view article find links to article

TVS. A normed space is a Banach space (that is, its canonical norm-induced metric is complete) if and only if it is complete as a topological vector space

Construction of a complex null tetrad (3,466 words) [view diff] exact match in snippet view article find links to article

a l b {\displaystyle g_{ab}+l_{a}n_{b}+n_{a}l_{b}} should span the induced metric h A B {\displaystyle h_{AB}} for cross-sections of {v=constant, r=constant}