If $\chi(M)=0$ then $M$ admits a nowhere-vanishing vector field
99230
If a manifold M has zero Euler characteristic, there is a non-vanishing vector field on it
96355
What is the first order axiom characterizing a field having characteristic zero?
33891
If $\mathbf A$ and $\mathbf B$ are Hermitian, when does $\det(\mathbf A-\lambda\mathbf B)=0$ have only real roots?
33190
Show that the complex integral is zero for any closed, piece wise smooth path
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
144745
Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
54500
Is the continuity of a vector field enough for the existence of the solution of a differential equation?
121830
The commutators of related vector fields are related
1162
Why $\{\mathbf{0}\}$ has dimension zero?
47977
If $u$ is harmonic and bounded in $0 < |z| < \rho$, show that the origin is a removable singularity
25039
Zero vector of a vector space
53848
$f$ holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0],$ then $0$ removable
27675
Polynomials vanishing on an infinite set
112114
Detailed proof that no essential singularity at infinity implies polynomial
56543
Do we fix divergence of the vector potential $A$, because $\nabla \cdot \nabla \psi \ne 0$?
149822
If $\omega \in \Omega^q(M)$, and $(\omega|_{U})_p = 0$, is $\omega_p = 0$?
88311
Linear functional f(v)=0 imply v=0