A Classification of Twisted Austere 3-Folds

Autor: Spiro Karigiannis, Thomas A. Ivey

Publikováno v: Symmetry, Integrability and Geometry: Methods and Applications.

A twisted-austere $k$-fold $(M, \mu)$ in $\mathbb R^n$ consists of a $k$-dimensional submanifold $M$ of $\mathbb R^n$ together with a closed $1$-form $\mu$ on $M$ such that the 'twisted conormal bundle' $N^* M + d \mu$ is a special Lagrangian submani

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::03e9821bcb07eee78564cdd0fb577a03
https://doi.org/10.3842/sigma.2021.023

Maurer-Cartan Forms for Fields on Surfaces: Application to Heart Fiber Geometry

Autor: Jon Sporring, Emmanuel Piuze, Kaleem Siddiqi

Publikováno v: IEEE Transactions on Pattern Analysis and Machine Intelligence. 37:2492-2504

We study the space of first order models of smooth frame fields using the method of moving frames. By exploiting the Maurer-Cartan matrix of connection forms we develop geometrical embeddings for frame fields which lie on spherical, ellipsoidal and g

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cdd775394a0d25c4b1c6de11d189cdd8
https://doi.org/10.1109/tpami.2015.2408352

Ruled austere submanifolds of dimension four

Autor: Thomas A. Ivey, Marianty Ionel

Publikováno v: Differential Geometry and its Applications. 30:588-603

We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. The algebraic possibilities for second fundamental forms of an austere 4-fold M were classified by Bryant, falling into three types which we label A, B, and C. We sh

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https://doi.org/10.1016/j.difgeo.2012.07.007

A New Method of CMM Inspect Path Planning for Precision Generalized Helicoid

Autor: Wei Min Pan, Yong Jian Yu, Jishun Li, Feng Xu

Publikováno v: Key Engineering Materials. 455:458-461

The helical surfaces are widely applied to both power transmission and fluid compression or pumping. Helicoid is measured by digitized measurement with the coordinate measuring machine (CMM) in this paper. A numerical measuring method which is differ

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https://doi.org/10.4028/www.scientific.net/kem.455.458

Atlases of cardiac fiber differential geometry

Autor: Gustav J. Strijkers, Adrianus J. Bakermans, Kaleem Siddiqi, Emmanuel Piuze, Herve Lombaert, Jon Sporring

Publikováno v: Functional Imaging and Modeling of the Heart-7th International Conference, FIMH 2013, Proceedings, 442-449
STARTPAGE=442;ENDPAGE=449;TITLE=Functional Imaging and Modeling of the Heart-7th International Conference, FIMH 2013, Proceedings
Functional Imaging and Modeling of the Heart ISBN: 9783642388989
FIMH

Studies of intra-species cardiac fiber variability tend to focus on first-order measures such as local fiber orientation. Recent work has shown that myofibers bundle locally into a particular type of minimal surface, the generalized helicoid model (G

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ce13b9698346acaece063289c812e992
https://pure.amc.nl/en/publications/atlases-of-cardiac-fiber-differential-geometry(3e4cddbf-3f18-4466-8dab-b87c218a8264).html