# Volume 22

## Sectional Curvature in Riemannian Manifolds » NB CDF PDF

Published March 19, 2020

The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart. Encoded in this metric is the sectional curvature, which is often of interest to mathematical physicists, differential geometers and geometric group theorists alike. In this article, we provide a function to compute the sectional curvature for a Riemannian manifold given its metric tensor. We also define a function to obtain the Ricci tensor, a closely related object. Read More »
{"ft_lang_label":"__label__en","ft_lang_prob":0.93159354,"math_prob":0.73255336,"size":619,"snap":"2020-10-2020-16","text_gpt3_token_len":130,"char_repetition_ratio":0.13333334,"word_repetition_ratio":0.0,"special_character_ratio":0.1825525,"punctuation_ratio":0.09615385,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9890354,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-03-29T08:27:05Z\",\"WARC-Record-ID\":\"<urn:uuid:e03c0ae8-47e5-40ce-bccf-cedb0b20d03e>\",\"Content-Length\":\"21189\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:35500c79-04c3-4dcf-980e-26dc552e3dff>\",\"WARC-Concurrent-To\":\"<urn:uuid:ec2ae8a4-2609-49d6-9388-260ee50dc885>\",\"WARC-IP-Address\":\"140.177.205.75\",\"WARC-Target-URI\":\"https://www.mathematica-journal.com/volume/v22/\",\"WARC-Payload-Digest\":\"sha1:RMM6P54KQ44YAQKRDS5PAHGIVNNYWUSF\",\"WARC-Block-Digest\":\"sha1:PBL4RXBFT7K7SMVK7QBNDQQV7BJ3O3CY\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370494064.21_warc_CC-MAIN-20200329074745-20200329104745-00473.warc.gz\"}"}