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I'm trying to read section 3 in J. Jost and Y.L. Xin [JX], This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let $M$ be a locally symmetric Riemannian manifold. Let $c$ be a geodesic in $M$ and let $J$ be a Jacobi field along $c$. Let $\cdot$ be the derivative (differential) of $c$ and assume $J$ is orthogonal to $\cdot$. Under these hypotheses is it the case that the Lie bracket, $[\cdot, J]$, is $0$? If so, why?

[JX] title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}.

I would like to include a one-page LaTeX article and a screen shot to help explain my question but I don't know how to do that.

I'm trying to read section 3 in J. Jost and Y.L. Xin [JX]. This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let $M$ be a locally symmetric Riemannian manifold. Let $c$ be a geodesic in $M$ and let $J$ be a Jacobi field along $c$. Let $\cdot$ be the derivative (differential) of $c$ and assume $J$ is orthogonal to $\cdot$. Under these hypotheses is it the case that the Lie bracket, $[\cdot, J]$, is $0$? If so, why?

[JX] title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}.

I would like to include a one-page LaTeX article and a screen shot to help explain my question but I don't know how to do that.

I'm trying to read section 3 in J. Jost and Y.L. Xin [JX], This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let $M$ be a locally symmetric Riemannian manifold. Let $c$ be a geodesic in $M$ and let $J$ be a Jacobi field along $c$. Let $\cdot$ be the derivative (differential) of $c$ and assume $J$ is orthogonal to $\cdot$. Under these hypotheses is it the case that the Lie bracket, $[\cdot, J]$, is $0$? If so, why?

[JX] title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}.

I'm trying to read section 3 in J. Jost and Y.L. Xin [JX], This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let $M$ be a locally symmetric Riemannian manifold. Let $c$ be a geodesic in $M$ and let $J$ be a Jacobi field along $c$. Let $\cdot$ be the derivative (differential) of $c$ and assume $J$ is orthogonal to $\cdot$. Under these hypotheses is it the case that the Lie bracket, $[\cdot, J]$, is $0$? If so, why?

[JX] title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}.

I would like to include a one-page LaTeX article and a screen shot to help explain my question but I don't know how to do that.

I'm trying to read section 3 in J. Jost and Y.L. Xin, title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}. This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let M be a locally symmetric Riemannian manifold. Let c be a geodesic in M and let J be a Jacobi field along c. Let cdot be the derivative (differential) of c and assume J is orthogonal to cdot. Under these hypothees is it the case that the Lie bracket, [cdot, J], is 0? If so, why?

I'm trying to read section 3 in J. Jost and Y.L. Xin [JX], This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let $M$ be a locally symmetric Riemannian manifold. Let $c$ be a geodesic in $M$ and let $J$ be a Jacobi field along $c$. Let $\cdot$ be the derivative (differential) of $c$ and assume $J$ is orthogonal to $\cdot$. Under these hypotheses is it the case that the Lie bracket, $[\cdot, J]$, is $0$? If so, why?

[JX] title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}.