vti_encoding:SR|utf8-nl vti_author:SR|Slim-PC\\SlimSly vti_modifiedby:SR|Slim-PC\\SlimSly vti_timelastmodified:TR|19 Apr 2016 12:57:05 -0000 vti_timecreated:TR|19 Apr 2016 10:45:27 -0000 vti_title:SR|On The Generalized Gaussian and Mean curvatures in E₁ⁿ⁺¹ vti_extenderversion:SR|12.0.0.0 vti_backlinkinfo:VX| vti_nexttolasttimemodified:TW|19 Apr 2016 12:56:29 -0000 vti_cacheddtm:TX|19 Apr 2016 12:57:05 -0000 vti_filesize:IR|9619 vti_cachedtitle:SR|On The Generalized Gaussian and Mean curvatures in E₁ⁿ⁺¹ vti_cachedbodystyle:SR| vti_cachedlinkinfo:VX|H|favicon.ico Q|default.css Q|headerpicture.css S|images/sjp_logo.jpg A|search.php H|http://www.sjpub.org H|http://www.sjpub.org/journals.html H|http://www.sjpub.org/sjms.html H|http://www.sjpub.org/submit.html H|http://www.sjpub.org/sjeeditorial.html H|http://www.sjpub.org/aboutus.html H|http://www.sjpub.org/contactus.html H|http://creativecommons.org/licenses/by/3.0/ H|http://www.sjpub.org/sjms/sjms-111.pdf H|http://www.sjpub.org/sjms.html D|clsid:D27CDB6E-AE6D-11cf-96B8-444553540000 D|http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab S|Journal-Cover.swf S|Journal-Cover.swf H|http://www.sjpub.org/sje-index.html H|http://www.sjpub.org/sje-bibliographic.html H|http://www.sjpub.org/sjms-aim.html H|http://www.sjpub.org/sjms.html H|http://www.sjpub.org/sjmseditorial.html H|http://www.sjpub.org/contactus.html H|http://www.sjpub.org/publishwithus.html H|http://www.sjpub.org/authorguide.html H|http://www.sjpub.org/submit.html H|http://www.sjpub.org/authorfaq.html H|http://www.sjpub.org/joineditors.html H|http://www.sjpub.org/joinreviewers.html H|http://www.sjpub.org/sitemap.html vti_cachedsvcrellinks:VX|NHUS|sjms/abstract/favicon.ico FQUS|sjms/abstract/default.css FQUS|sjms/abstract/headerpicture.css FSUS|sjms/abstract/images/sjp_logo.jpg NAUS|sjms/abstract/search.php NHHS|http://www.sjpub.org NHHS|http://www.sjpub.org/journals.html NHHS|http://www.sjpub.org/sjms.html NHHS|http://www.sjpub.org/submit.html NHHS|http://www.sjpub.org/sjeeditorial.html NHHS|http://www.sjpub.org/aboutus.html NHHS|http://www.sjpub.org/contactus.html NHHS|http://creativecommons.org/licenses/by/3.0/ NHHS|http://www.sjpub.org/sjms/sjms-111.pdf NHHS|http://www.sjpub.org/sjms.html NDUS|clsid:D27CDB6E-AE6D-11cf-96B8-444553540000 NDHS|http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab FSUS|sjms/abstract/Journal-Cover.swf FSUS|sjms/abstract/Journal-Cover.swf NHHS|http://www.sjpub.org/sje-index.html NHHS|http://www.sjpub.org/sje-bibliographic.html NHHS|http://www.sjpub.org/sjms-aim.html NHHS|http://www.sjpub.org/sjms.html NHHS|http://www.sjpub.org/sjmseditorial.html NHHS|http://www.sjpub.org/contactus.html NHHS|http://www.sjpub.org/publishwithus.html NHHS|http://www.sjpub.org/authorguide.html NHHS|http://www.sjpub.org/submit.html NHHS|http://www.sjpub.org/authorfaq.html NHHS|http://www.sjpub.org/joineditors.html NHHS|http://www.sjpub.org/joinreviewers.html NHHS|http://www.sjpub.org/sitemap.html vti_cachedneedsrewrite:BR|false vti_cachedhasbots:BR|false vti_cachedhastheme:BR|false vti_cachedhasborder:BR|false vti_metatags:VR|HTTP-EQUIV=Content-Type text/html;\\ charset=iso-8859-1 citation_author Ayse\\ Yavuz,\\ \\ F.\\ Nejat\\ Ekmekci citation_title On\\ The\\ Generalized\\ Gaussian\\ and\\ Mean\\ curvatures\\ in\\ E₁ⁿ⁺¹ citation_pdf_url http://www.sjpub.org/sjms/sjms-111.pdf citation_year 2016 citation_online_date 2016 citation_journal_title Science\\ Journal\\ of\\ Mathematics\\ and\\ Statistics citation_abstract Before\\ now\\ in\\ [2]\\ the\\ generalized\\ Gaussian\\ and\\ mean\\ curvatures\\ were\\ proved\\ in\\ Euclidean\\ space,\\ but\\ now\\ we\\ prove\\ the\\ theorems\\ in\\ Lorentzian\\ Space.\\ In\\ our\\ previous\\ paper,\\ we\\ have\\ studied\\ higher\\ order\\ Gaussian\\ curvatures\\ in\\ Lorentzian\\ space.\\ \r\n This\\ allowed\\ us\\ to\\ prove\\ that\r\nφ(P)=\\ ∏_(i=1)^n▒(1+ε_i\\rk_i\\\\ )\\ \r\nIn\\ addition\\ to\\ Gaussian\\ and\\ mean\\ curvatures,\\ K_r\\ and\\ H_r\\ for\\ parallel\\ surfaces\\ in\\ E_1^3\\ are\\ given.\\ In\\ this\\ study\\ by\\ means\\ of\\ higher\\ order\\ Gaussian\\ and\\ mean\\ curvatures\\ we\\ calculate\\ the\\ generalized\\ curvatures\\ K_r\\ and\\ H_r\\ for\\ parallel\\ surfaces\\ in\\ E_1^(n+1).\r\n dc.rights http://creativecommons.org/licenses/by/3.0/ citation_volume 2016 citation_publisher Science\\ Journal\\ Publication citation_issn 2276-6324 citation_abstract_html_url http://www.sjpub.org/sjms/abstract/sjms-111.html vti_charset:SR|iso-8859-1