Let $H$ be hyperbolic 3-space. Let $TH$ be the tangent bundle of $H$. I have a question:
Is $TH$ isometric to H times a flat $k$-space?
2025-01-12 23:59:17.1736726357
Is the tangent bundle of hyperbolic space trivial?
158 Views Asked by Muniain https://math.techqa.club/user/muniain/detail AtRelated Questions in MANIFOLDS
- Find the interior product of a basic p-form $\alpha = dx_1 \wedge dx_2 \wedge \ldots \wedge dx_p$ and a vector field $X$
- Every Manifold is Locally Path Connected
- Connect Sum of a connected, compact manifold of dimension n and $S^n$
- homeomorphism of the closed disc on $\mathbb R ^2$
- Showing that the Mapping Torus is a topological manifold
- Suggestion for reference book for differential forms, differentiable manifolds and other topics
- Does every torus $T\subset S^3$ bounds a solid tours $S^1\times D^2\subset S^3$?
- Is a smooth function still smooth in a sub-manifold containing its image?
- The Developing Map
- How to compute that $\mathcal{L}_Vg_{ij}=g_{ik}\nabla_jV^k+g_{jk}\nabla_iV^k$
Related Questions in HYPERBOLIC-GEOMETRY
- Triangle inequality of hyperbolic metric
- Is the tangent bundle of hyperbolic space trivial?
- Outer Automorphisms of PSL2(R)
- Finitely Many genus-g Quotients of Compact Riemann Surface
- Applications of the Hurwitz Theorem on Number of Automorphisms?
- Why does the halfplane model of the hyperbolic plane involve only the upper half of the plane?
- "Every geometry is a projective geometry." So is hyperbolic geometry a projective geometry?
- Algebraic solutions for Poincaré Disk arcs
- The precise formula of the Poincare-Bergman metric on the disc $\mathbb{D}$.
- Law of Cosines with imaginary arguments?
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