Simson-Wallace locus in d-dimensional projective - metric space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F17%3A43896293" target="_blank" >RIV/60076658:12410/17:43896293 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs00022-016-0346-y.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs00022-016-0346-y.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00022-016-0346-y" target="_blank" >10.1007/s00022-016-0346-y</a>
Alternative languages
Result language
angličtina
Original language name
Simson-Wallace locus in d-dimensional projective - metric space
Original language description
We generalize the Simson-Wallace locus in d-dimensional projective metric space, i.e. we look for the points whose orthogonal projections onto the hyperplanes of a fixed d-simplex lie on a hyperplane d -1 plane. We show that this Simson-Wallace locus is a (hyper)surface of d+1 degree, if the metric hyperplane point polarity is non-degenerate, e.g. in spherical and hyperbolic d-spaces, respectively. Else it splits by the ideal hyperplane of poles of the simplex hyperplanes, e.g. into this ideal hyperplane and a remaining d-degree surface, e.g. in the Euclidean d-space. Our seemingly new general method is based on the starting concepts of the Grassmann-Clifford exterior algebra calculus.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Geometry
ISSN
0047-2468
e-ISSN
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Volume of the periodical
108
Issue of the periodical within the volume
2
Country of publishing house
CH - SWITZERLAND
Number of pages
17
Pages from-to
393-409
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-84983738592