Complex manifold

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Implications of complex structure

Smooth functions Smooth Compact Algebraic varieties Smooth manifolds

15 related topics

Almost complex structures

Almost complex structure G-structures Linear complex structure Endomorphism Tangent bundle

13 related topics

Kähler and Calabi–Yau manifolds

Riemannian metric Hermitian metric Skew-symmetric Symplectic Closed

13 related topics

Examples of complex manifolds

Calabi–Yau manifolds Algebraic varieties Complex projective spaces Grassmannians Lie groups

9 related topics

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Implications of complex structure

Smooth functions Smooth function
Smooth Smooth manifold
Compact Compact space
Algebraic varieties Algebraic variety
Smooth manifolds Differentiable manifold
Real-analytic manifolds Analytic manifold
Whitney embedding theorem
Embedded Embedding
The maximum modulus principle Maximum modulus principle
Stein manifolds Stein manifold
Smooth structures Smooth structure
Riemann surfaces Riemann surface
Genus Genus (mathematics)
Moduli space
Orientable

Examples of complex manifolds

Calabi–Yau manifolds Calabi–Yau manifold
Algebraic varieties
Complex projective spaces Complex projective space
Grassmannians Grassmannian
Lie groups
Simply connected
Disk Disk (mathematics)
Riemann sphere
Liouville's theorem Liouville's theorem (complex analysis)

Disc vs. space vs. polydisc

Almost complex structures

Almost complex structure
G-structures G-structure
Linear complex structure
Endomorphism
Tangent bundle
Integrable Frobenius theorem (differential topology)
Nijenhuis tensor
Sphere Hypersphere
Orthogonal complement
Octonions Octonion
Heinz Hopf
Complex numbers Complex number
Newlander–Nirenberg theorem

Kähler and Calabi–Yau manifolds

Riemannian metric
Hermitian metric
Skew-symmetric Skew-symmetric bilinear form
Symplectic Symplectic geometry
Closed Closed and exact differential forms
Nondegenerate Nondegenerate form
Kähler manifolds Kähler manifold
Projective varieties
Hopf manifolds Hopf manifold
Betti number
Hodge theory
Ricci-flat Ricci-flat manifold
Chern class

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Map overview Semantic statistics

Nodes69

Edges68

Triples50

Avg. degree1.97

Density0.028986

Components1

How this topic connects Entity context

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Complex manifold

Top relations

related to Implications of complex structure · 10

Complex manifold → Cn, Complex, Consider, For, In, Now, R2n, Since, Stein, Whitney

related to References · 10

Complex manifold → Classics, Complex Manifolds, Complex Structures, Deformation, ISBN, Kodaira, Kunihiko, Mathematics, November, Springer

related to Kähler and Calabi–Yau manifolds · 8

Complex manifold → As, Hermitian, If, Kähler, Like, One, Riemannian, The

related to Smooth complex algebraic varieties · 7

Complex manifold → Complex, Complex Grassmannians, Complex Lie, GL, Pn, Smooth, Sp

related to Examples of complex manifolds · 5

Complex manifold → Calabi, Riemann, The, The Cartesian, Yau

related to Almost complex structures · 4

Complex manifold → An, Concretely, G-structures, GL

related to Simply connected · 3

Complex manifold → CC, Riemann, The

related to Disc vs. space vs. polydisc · 1

Complex manifold → The

see also · 1

Complex manifold → Complex

Important terminology Word statistics

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Important terminology

complex manifold manifolds structure almost smooth holomorphic kähler space structures integrable example called algebraic varieties real one unit maps sense

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
GL	instance of	Complex Grassmannians.Complex Lie groups	0.80	text
Complex manifold	related to Almost complex structures	An	0.60	section
Complex manifold	related to Almost complex structures	GL	0.60	section
Complex manifold	related to Almost complex structures	G-structures	0.60	section
Complex manifold	related to Almost complex structures	Concretely	0.60	section
Complex manifold	related to Disc vs. space vs. polydisc	The	0.60	section
Complex manifold	related to Examples of complex manifolds	Riemann	0.60	section
Complex manifold	related to Examples of complex manifolds	Calabi	0.60	section
Complex manifold	related to Examples of complex manifolds	Yau	0.60	section
Complex manifold	related to Examples of complex manifolds	The Cartesian	0.60	section
Complex manifold	related to Examples of complex manifolds	The	0.60	section
Complex manifold	related to Implications of complex structure	Since	0.60	section

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Min side: 3

Research this topic

Explore this topic

Implications of complex structure

Almost complex structures

Kähler and Calabi–Yau manifolds

Examples of complex manifolds

Key facts & relationships

Topics to explore

Overview

Implications of complex structure

Examples of complex manifolds

Disc vs. space vs. polydisc

Almost complex structures

Kähler and Calabi–Yau manifolds

Advanced semantic analysis

Map overview Semantic statistics

Complex manifold

How this topic connects Entity context

Complex manifold

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges