How many height function on a given compact oriantable manifold there exist up to $SO(n)$ rotations? It seems to me that there is only one height function, but I have no Idea how to show it.
2026-03-26 19:17:13.1774552633
How many height function on a given compact oriantable manifold there exist up to $SO(n)$ rotations?
20 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SMOOTH-MANIFOLDS
- Smooth Principal Bundle from continuous transition functions?
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- "Defining a smooth structure on a topological manifold with boundary"
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- A finite group G acts freely on a simply connected manifold M
- An elementary proof that low rank maps cannot be open
- What does it mean by standard coordinates on $R^n$
- Partial Differential Equation using theory of manifolds
- Showing that a diffeomorphism preserves the boundary
Related Questions in ROTATIONS
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- why images are related by an affine transformation in following specific case?(background in computer vision required)
- Proving equations with respect to skew-symmetric matrix property
- Finding matrix linear transformation
- A property of orthogonal matrices
- Express 2D point coordinates in a rotated and translated CS
- explicit description of eigenvector of a rotation
- Finding the Euler angle/axis from a 2 axes rotation but that lies on the original 2 axes' plane
- How to find a rectangle's rotation amount that is inscribed inside an axis-aligned rectangle?
- Change of basis with rotation matrices
Related Questions in MORSE-THEORY
- Morse index of minimal surfaces in $\mathbb{R}^3$
- Understanding Morse's Lemma
- A closed manifold has closed geodesics of at most countably many lengths
- Codimension-1 submanifold as a inverse image of regular value.
- A Morse function on a compact manifold has finitely many critical points
- Equivalence between function being Morse and $df$ being transversal to zero section.
- Morse lemma via Moser's trick
- The Euler characteristic of a manifold
- How is a condition on symplectic triviality expressed in Chern classes?
- Proving $\partial ^ 2 = 0 $ for the case of Morse-Complex with $\mathbb{Z}$ using orientation of the moduli space
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- 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?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- 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
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?