My problem is on the definition of the Hodge star operator on Riemann surface $S$. In general the definition of an Hodge star operator on a manifold depend of the metric but on Riemann surfaces the definitions are saying $\star dz=-id{z}$ and $\star d\overline{z}=id\overline{z}$. So I guess that there is a unique (or canonical) metric one Riemann surface? Can you explain me that or/and give me a good reference for beginner in such a subject. Thanks!
2026-03-26 06:34:22.1774506862
Hodge star operator independant from hermitian metric
201 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in COMPLEX-GEOMETRY
- Numerable basis of holomporphic functions on a Torus
- Relation between Fubini-Study metric and curvature
- Hausdorff Distance Between Projective Varieties
- What can the disk conformally cover?
- Some questions on the tangent bundle of manifolds
- Inequivalent holomorphic atlases
- Reason for Graphing Complex Numbers
- Why is the quintic in $\mathbb{CP}^4$ simply connected?
- Kaehler Potential Convexity
- I want the pullback of a non-closed 1-form to be closed. Is that possible?
Related Questions in RIEMANN-SURFACES
- Composing with a biholomorphic function does not affect the order of pole
- open-source illustrations of Riemann surfaces
- I want the pullback of a non-closed 1-form to be closed. Is that possible?
- Reference request for Riemann Roch Theorem
- Biholomorphic Riemann Surfaces can have different differential structure?
- Monodromy representations and geodesics of singular flat metrics on $\mathbb{H}$
- How to choose a branch when there are multiple branch points?
- Questions from Forster's proof regarding unbranched holomorphic proper covering map
- Is the monodromy action of the universal covering of a Riemann surface faithful?
- Riemann sheets for combined roots
Related Questions in HODGE-THEORY
- How are rational algebraic Hodge classes of type $ (p,p) $ defined?
- Why $H_{dR}^1(M) \simeq \mathbb R^n$ when $H_1(M,\mathbb Z)$ has $n$ generators?
- Regarding Hodge's theorem
- Let $M$ is compact Riemann surface, if $\omega$ is a 2-form and $\int_{M} \omega =0$ then there exists a smooth function $f$ such that $\omega=d*df$
- Commutation of the covariant Hodge Laplacian with the covariant derivative
- Every $L^2$ function is the divergence of a $L^2$ vector field
- Question in proof of Hodge decomposition theorem
- Lefschetz (1,1) theorem for quasi-projective varieties
- Local invariant cycles with integer coefficients
- Sign of codifferential
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?