Skip to main content
Bumped by Community user
edited for a more thorough conclusion
Source Link

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_{n-1}:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line passing through the origin contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_{n-1}:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_{n-1}:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line passing through the origin contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

added 4 characters in body
Source Link

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_n:=G_{n-1}(\mathbb{R}^n)$$G_{n-1}:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_n:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_{n-1}:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

added 6 characters in body
Source Link

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_n:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in $G_{n-1}$that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_n:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in $G_{n-1}$ belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

I am currently working on some problems related to Grassmann manifolds and eventually come to the following question.

Let $S$ be a subset of $G_1(\mathbb{R}^n)$ such that any element of $G_n:=G_{n-1}(\mathbb{R}^n)$ contains a line in $S.$ Is it true that there exists a hyperplane in $G_{n-1}$ that is completely covered by $S$ (that is, every line contained in that hyperplane belongs to $S$)?

Has this problem ever been discussed before? So far I could not come up with any good idea for it, at least not by "geometric arguments".

Improved grammar/wording
Source Link
Manuel Bärenz
  • 5.6k
  • 18
  • 49
Loading
Source Link
Loading