English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study some basic properties of the function $f_0:M\rightarrow\IR$ onHadamard manifolds defined by $$ f_0(x):=\langleu_0,\exp_{x_0}^{-1}x\rangle\quad\mbox{for any $x\in M$}. $$ A characterizationfor the function to be linear affine is given and a counterexample onPoincar\'e plane is provided, which in particular, shows that assertions (i)and (ii) claimed in \cite[Proposition 3.4]{Papa2009} are not true, and that thefunction $f_0$ is indeed not quasi-convex. Furthermore, we discuss theconvexity properties of the sub-level sets of the function on Riemannianmanifolds with constant sectional curvatures.

On Some Basic Results Related to Affine Functions on Riemmanian Manifolds