Let $M$ be a real Riemannian manifold of even dimension, what are the advantages of considering an almost complex structure on it rather than only real?
2025-01-13 05:29:47.1736746187
Advantage in considering an almost complex structure
75 Views Asked by user333046 https://math.techqa.club/user/user333046/detail AtRelated Questions in DIFFERENTIAL-GEOMETRY
- Are Christoffel symbols invariant under reparameterization of the curve?
- Tangent bundle equivalence not a pushforward
- Find the interior product of a basic p-form $\alpha = dx_1 \wedge dx_2 \wedge \ldots \wedge dx_p$ and a vector field $X$
- Showing Hofer's metric is bi-invariant
- What does it mean to 'preserve the first fundamental form'?
- proving a given curve is a geodesic
- Find the area of a double lune
- Commuting Covariant Derivatives in Derivation of First Variation Formula
- Every diffeomorphism which is an isometry is also conformal
- How do I make sense of terms $X^j\partial_j(Y^i)$ in the Lie bracket of vector fields?
Related Questions in RIEMANNIAN-GEOMETRY
- Are Christoffel symbols invariant under reparameterization of the curve?
- proving a given curve is a geodesic
- Commuting Covariant Derivatives in Derivation of First Variation Formula
- starry regular icosahedron
- How to compute that $\mathcal{L}_Vg_{ij}=g_{ik}\nabla_jV^k+g_{jk}\nabla_iV^k$
- Sign of Riemannian and application of commutating formula .
- Definition of Riemannian Metric
- The linearization of a system and the derivative of operator.
- Compute of metric and curvature under transformation of coordinates.
- proving a particular subset of a Riemannian manifold is closed using continuity
Related Questions in SMOOTH-MANIFOLDS
- Tangent bundle equivalence not a pushforward
- Find the interior product of a basic p-form $\alpha = dx_1 \wedge dx_2 \wedge \ldots \wedge dx_p$ and a vector field $X$
- How do I make sense of terms $X^j\partial_j(Y^i)$ in the Lie bracket of vector fields?
- Is a smooth function still smooth in a sub-manifold containing its image?
- Sign of Riemannian and application of commutating formula .
- Is an integral manifold N of a distribution $\Delta$ over M always a submanifold of M?
- Infinite connected sum of S^n
- Characterization of Tangent Space as Quotient space of Vector Fields
- Smooth diffeomorphism and $C^1$ diffeomorphism
- The Riemannian Distance function does not change if we use $C^1$ paths?
Related Questions in COMPLEX-GEOMETRY
- Equality $H^i(K,\mathcal{F}_{|K})=\varinjlim_{U\supset K}H^i(U,\mathcal{F}_{|U})$ for a constructible sheaf
- Question about Gysin map (pushforward in cohomology)
- When do vector bundles decompose into line bundles?
- Definition of a Subtorus
- Base change of topogical spaces VS Base change of schemes
- Complex differential forms on $CP^n$
- Is there a complex surface into which every Riemann surface embeds?
- Extending a d-closed (p,q) form of a fibre of complex analytic family
- Why care about (local) rational functions in algebraic geometry?
- cohomology of a tangent bundle
Related Questions in ALMOST-COMPLEX
- Curvature identity on Nearly Kähler manifolds
- Find type of a differential form on an almost complex manifold
- Fibration induced by an almost complex structure
- When does contractible space of almost complex structures taming a given symplectic form $\omega$ contain an integrable compatible one?
- Pulling back a Kähler structure on a symplectic submanifold
- Identification of the holomorphic tangent space with the real tangent space
- Almost complex manifolds are orientable
- Advantage in considering an almost complex structure
- Complex and Conformal structure on a trivial tangent bundle of a higher dimensional manifold
- What does it mean for an almost complex structure to be compatible with a Riemannian metric?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity